Vintage Toy Record Player
I had an earlier version of one of these vintage toy record players when I was a kid--They're great! Not just because it gives your kid something to play with, but because it's perfect for a distraction when your young toddler starts getting grabby with your personal prized record collection.
Anybody that might have had one of the originals growing up will probably see this one as a little less substantial as the ones from 30+ years ago, but this thing will do the trick for your kid. If you're raising your kid around your own energy for playing music and records, this will be a welcome diversion.
Soundtracks and Kids vinyl
And then, of course, if your kid is a little bit older, a great way to fuel the flame of their interest in vinyl and record players beyond a toy record player... you could start getting them LPs that they'd be more obviously interested in. Personally, I've found the movie soundtracks are great to get kids interested and requesting music on their own. You might get exhausted from them in short order, but your kids will listen to these exhaustively.