Encourage the joints to root. That makes the whole plant stronger and more resistant to disease and insects. You might keep the grass away as best you can. When you water (if you need to), water along the whole rooted vine. I had some giant squash vines last year that had SVB’s in them. The SVB infected part died, of course, but the rest of the rooted vine survived and produced just fine. The vines we allowed to root and grow along the ground out produced the trellised ones by a factor of about 2:1. This is only with vining things that will root along the vine. IIRC, cucumbers and melons don’t do this. We trellis those.
Your little pumpkin looks great! Give it time, allow it to root where it wants (I direct the unrooted tips where I want them to go) and when you fertilize (I use compost tea), sprinkle some along the vine also. You’ll get female blooms eventually. They’ll look like teeny little pumpkins with a flower on the end.
Good luck!