1. Controller:

        using Microsoft.AspNetCore.Authentication;
        using Microsoft.AspNetCore.Authentication.Google;
        using Microsoft.AspNetCore.Authorization;
        using Microsoft.AspNetCore.Mvc;
        using Microsoft.VisualBasic;
        using System.Security.Claims;

        namespace GoogleAuthWithoutIdentity.Controllers
        {
            public class AccountController : Controller
            {
                public IActionResult Login()
                {
                    return View();
                }
                /// <summary>
                /// Google Login Redirection To Google Login Page
                /// </summary>
                /// <returns></returns>
                public IActionResult GoogleLogin()
                {
                    return new ChallengeResult(
                        GoogleDefaults.AuthenticationScheme,
                        new AuthenticationProperties
                        {
                            RedirectUri = Url.Action("GoogleResponse", "Account") // Where google responds back
                        });
                }
                /// <summary>
                /// Google Login Response After Login Operation From Google Page
                /// </summary>
                /// <returns></returns>
                public async Task<IActionResult> GoogleResponse()
                {
                    //Check authentication response as mentioned on startup file as o.DefaultSignInScheme = "External"
                    var authenticateResult = await HttpContext.AuthenticateAsync("External");
                    if (!authenticateResult.Succeeded)
                        return BadRequest(); // TODO: Handle this better.
                    //Check if the redirection has been done via google or any other links
                    if (authenticateResult.Principal.Identities.ToList()[0].AuthenticationType.ToLower() == "google")
                    {
                        //check if principal value exists or not 
                        if (authenticateResult.Principal != null)
                        {
                            //get google account id for any operation to be carried out on the basis of the id
                            var googleAccountId = authenticateResult.Principal.FindFirst(ClaimTypes.NameIdentifier)?.Value;
                            //claim value initialization as mentioned on the startup file with o.DefaultScheme = "Application"
                            var claimsIdentity = new ClaimsIdentity("Application");
                            if (authenticateResult.Principal != null)
                            {
                                //Now add the values on claim and redirect to the page to be accessed after successful login
                                var details = authenticateResult.Principal.Claims.ToList();
                                claimsIdentity.AddClaim(authenticateResult.Principal.FindFirst(ClaimTypes.NameIdentifier));// Full Name Of The User
                                claimsIdentity.AddClaim(authenticateResult.Principal.FindFirst(ClaimTypes.Email)); // Email Address of The User
                                await HttpContext.SignInAsync("Application", new ClaimsPrincipal(claimsIdentity));
                                return RedirectToAction("Index", "Home");
                            }
                        }
                    }
                    return RedirectToAction("Index", "Home");
                }
                /// <summary>
                /// Google Login Sign out
                /// </summary>
                /// <returns></returns>
                public async Task<IActionResult> SignOutFromGoogleLogin()
                { //Check if any cookie value is present
                    if (HttpContext.Request.Cookies.Count > 0)
                    { //Check for the cookie value with the name mentioned for authentication and delete each cookie
                        var siteCookies = HttpContext.Request.Cookies.Where(c => c.Key.Contains(".AspNetCore.") || c.Key.Contains("Microsoft.Authentication"));
                        foreach (var cookie in siteCookies)
                        {
                            Response.Cookies.Delete(cookie.Key);
                        }
                    }
                    //signout with any cookie present 
                    await HttpContext.SignOutAsync("External"); 
                    return RedirectToAction("Index", "Home");
                } 
            }
        }
2. Layout page:
 
        <body>
            <header>
                <nav class="navbar navbar-expand-sm navbar-toggleable-sm navbar-light bg-white border-bottom box-shadow mb-3">
                    <div class="container-fluid">
                        <a class="navbar-brand" asp-area="" asp-controller="Home" asp-action="Index">GoogleAuthWithoutIdentity</a>
                        <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target=".navbar-collapse" aria-controls="navbarSupportedContent"
                                aria-expanded="false" aria-label="Toggle navigation">
                            <span class="navbar-toggler-icon"></span>
                        </button>
                        <div class="navbar-collapse collapse d-sm-inline-flex justify-content-between">
                            <ul class="navbar-nav flex-grow-1">
                                <li class="nav-item">
                                    <a class="nav-link text-dark" asp-area="" asp-controller="Home" asp-action="Index">Home</a>
                                </li>
                                <li class="nav-item">
                                    <a class="nav-link text-dark" asp-area="" asp-controller="Home" asp-action="Privacy">Privacy</a>
                                </li>
                            </ul>
                <ul class="navbar-nav">
                    @if (User.Identity.IsAuthenticated)
                    {
                        <li class="nav-item">
                            <a class="nav-link text-dark" title="Manage">Hello @User.Claims.FirstOrDefault(c=>c.Type == "http://schemas.xmlsoap.org/ws/2005/05/identity/claims/emailaddress").Value!</a>
                        </li>
                        <li class="nav-item"> 
                            <a class="nav-link text-dark" asp-controller="Account" asp-action="SignOutFromGoogleLogin">SignOutFromGoogleLogin</a>
                        </li>
                    }
                    else
                    { 
                        <li class="nav-item">
                            <a class="nav-link text-dark" asp-controller="Account" asp-action="GoogleLogin">Google Login</a>
                        </li>
                    }
                </ul>
                        </div>
                    </div>
                </nav>
            </header>
            <div class="container">
                <main role="main" class="pb-3">
                    @RenderBody()
                </main>
            </div>

            <footer class="border-top footer text-muted">
                <div class="container">
                    &copy; 2022 - GoogleAuthWithoutIdentity - <a asp-area="" asp-controller="Home" asp-action="Privacy">Privacy</a>
                </div>
            </footer>
            <script src="~/lib/jquery/dist/jquery.min.js"></script>
            <script src="~/lib/bootstrap/dist/js/bootstrap.bundle.min.js"></script>
            <script src="~/js/site.js" asp-append-version="true"></script>
            @await RenderSectionAsync("Scripts", required: false)
        </body> 
3. Program.cs

        using Microsoft.AspNetCore.Authentication.Cookies;
        using Microsoft.AspNetCore.Authentication.Google;

        var builder = WebApplication.CreateBuilder(args);
        var configuration = builder.Configuration;
        // Add services to the container.
        builder.Services.AddControllersWithViews();
        builder.Services.AddAuthentication(o =>
            {
                o.DefaultScheme = "Application";
                o.DefaultSignInScheme = "External";
            })
            .AddCookie("Application")
            .AddCookie("External")
            .AddGoogle(googleOptions =>
            { 
                googleOptions.ClientId = configuration["GoogleAuth:ClientId"];
                googleOptions.ClientSecret = configuration["GoogleAuth:ClientSecret"];
            });
        var app = builder.Build();

        // Configure the HTTP request pipeline.
        if (!app.Environment.IsDevelopment())
        {
            app.UseExceptionHandler("/Home/Error");
            // The default HSTS value is 30 days. You may want to change this for production scenarios, see https://aka.ms/aspnetcore-hsts.
            app.UseHsts();
        }

        app.UseHttpsRedirection();
        app.UseStaticFiles();

        app.UseRouting();

        app.UseAuthentication();
        app.UseAuthorization();

        app.MapControllerRoute(
            name: "default",
            pattern: "{controller=Home}/{action=Index}/{id?}");

        app.Run();