Take a look at what games he plays if you have him added on Steam, or ask his favorites. You could try one of those in your free time to get the hang of it before asking him to play (if you felt anxious about that part XD). He'd probably be hype that you wanted to join him in his hobby!

There are also a ton of two person co-op games that you two could play together - I know your schedules are part of the problem, but if possible ever that might be fun. I played 'It Takes Two' with my boyfriend while we were long distance. It has cute animation and is pretty straightforward - puzzle solving to move through the game, but you both have to do your part in order to advance. Stardew Valley is also a good pick - you can farm together and build a little city.

Otherwise, start with what you like as there might be a game related.

Do you like horror?

Do you like decorating + creating?

Do you want to try a shooting game?

Do you want to play alone or play a team-based game?

What are your hobbies outside of gaming? I can try to make some suggestions for games you might like based off of that!