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.
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.