We just played an informal game that my daughter “invented” when she was about 3 years old. At first she would ask what letter every word started with. Then once she figured out most of the letter sounds, (with some help from Starfall as well,) she started reversing it and would ask me to tell her a word so she could figure out the beginning letter. Eventually we switched to the ending sounds, then middle. This was all before we did any formal work on reading.
You could easily introduce this type of play. Just a caution, though, it drove me crazy trying to think of new words for her all the time. She wanted to ‘play’ the game continuously when she was trying to learn how to read.