Where can I watch One Punch Man season 2 legally? I have checked Hulu, but it does not have episode 1 of One Punch Man season 2.

Where can I watch episode 1 to current legally?
You are in the United States of America (Texas) according to your profile.  Here, One Punch Man is being shown exclusively on Hulu.  

https://www.newsweek.com/one-punch-man-season-2-time-how-watch-1388310

Disregarding legal loopholes, that is the only place you can legally watch this show in the United States. I do not know why you were not able to find it.