How to get ready for rec season if you're a busy, chunky dad?

The temperatures here are slowly creeping up past -70 or whatever. Assuming my rec league team wants me back, what are some gentle ways to get ready for the season?

I'm thinking some stationary bike a few days a week (not a bad idea anyway), batting cages once every few weeks if possible.

I'm kinda fat and plan to remain so, TYVM. (Just saying this will continue the torrent of GLP-1 ads, I'm sure.) I'm also 40 and plan to remain so until I'm 41. I have a small child (small enough to require close supervision if coming to a batting cage) so free time is at a premium. And while it's no longer trans-Neptunian-object cold, it's still not going to be consistently nice out for a while. And please keep in mind, this is for rec league softball, a hobby that I enjoy but isn't what I base my self-worth on.

With all that, what are some ways that worked for people in similar situations? My goals are to be only kind of winded on the bases, maintain what's left of my limited agility, and not hurt myself in a long-term way. Any recommendations?