Solution in different C# versions

C# 8 with at least .NET Core 3.0 or .NET Standard 2.1

public static class StringExtensions
{
    public static string FirstCharToUpper(this string input) =>
        input switch
        {
            null => throw new ArgumentNullException(nameof(input)),
            "" => throw new ArgumentException($"{nameof(input)} cannot be empty", nameof(input)),
            _ => string.Concat(input[0].ToString().ToUpper(), input.AsSpan(1))
        };
}

Since .NET Core 3.0 / .NET Standard 2.1 String.Concat() supports ReadonlySpan<char> which saves one allocation if we use .AsSpan(1) instead of .Substring(1).

C# 8

public static class StringExtensions
{
    public static string FirstCharToUpper(this string input) =>
        input switch
        {
            null => throw new ArgumentNullException(nameof(input)),
            "" => throw new ArgumentException($"{nameof(input)} cannot be empty", nameof(input)),
            _ => input[0].ToString().ToUpper() + input.Substring(1)
        };
}

C# 7

public static class StringExtensions
{
    public static string FirstCharToUpper(this string input)
    {
        switch (input)
        {
            case null: throw new ArgumentNullException(nameof(input));
            case "": throw new ArgumentException($"{nameof(input)} cannot be empty", nameof(input));
            default: return input[0].ToString().ToUpper() + input.Substring(1);
        }
    }
}

Really old answers

public static string FirstCharToUpper(string input)
{
    if (String.IsNullOrEmpty(input))
        throw new ArgumentException("ARGH!");
    return input.First().ToString().ToUpper() + String.Join("", input.Skip(1));
}

This version is shorter. For a faster solution, take a look at Diego’s answer.

public static string FirstCharToUpper(string input)
{
    if (String.IsNullOrEmpty(input))
        throw new ArgumentException("ARGH!");
    return input.First().ToString().ToUpper() + input.Substring(1);
}

Probably the fastest solution is Darren’s (There’s even a benchmark) although I would change it’s string.IsNullOrEmpty(s) validation to throw an exception since the original requirement expects for a first letter to exist so it can be uppercased. Note that this code works for a generic string and not particularly on valid values from the Textbox.