This can be a stupid question but I am new whatsoever this.

I wish to produce a Home windows program that conveys having a database. Can there be any method of doing this with no user of my program need to use a database program like MySql?

I am likely to program it in C#.

You should use embedded databases like SQLite or Firebird Embedded.

You'll find the entire listing of embedded database solutions on wikipedia page

SQL Server Compact matches your needs. However it does not support some benefits. But you don't have to use a seperate database server. It really works embedded.

Because you mention MySQL: MySQL Embedded Database

(It isn't free, though.)