QueueBuild.cs

using System;
using System.Linq;
using System.Threading.Tasks;
using Microsoft.TeamFoundation.Build.WebApi;
using Microsoft.VisualStudio.Services.Common;

class Program
{
    static void Main(string[] args)
    {
        QueueBuild("https://<yourdomain>.VisualStudio.com/DefaultCollection/", "<username>", "<password>", "<project>", "<BuildDefinitionname>").GetAwaiter().GetResult();
        Console.ReadLine();
    }

    static async Task QueueBuild(string url, string userName, string password, string project, string buildDefinitionName)
    {
        var build = new BuildHttpClient(new Uri(url), new VssBasicCredential(userName, password));
            
        // First we get project's GUID and buildDefinition's ID.
        // Get the list of build definitions.
        var definitions = await build.GetDefinitionsAsync(project: project);

        // Get the specified name of build definition.
        var target = definitions.First(d => d.Name == buildDefinitionName);
            
        // Build class has many properties, hoqever we can set only these properties.
        //ref: https://www.visualstudio.com/integrate/api/build/builds#queueabuild
        //In this nuget librari, we should set Project property.
        //It requires project's GUID, so we're compelled to get GUID by API.
        var res = await build.QueueBuildAsync(new Build
        {
            Definition = new DefinitionReference
            {
                Id = target.Id
            },
            Project = target.Project
        });
        Console.WriteLine($"Queued build with id: {res.Id}");
    }
}