Have a full meal before hand. Being hungry and overstimulated is the worst combination in the world. Being hydrated would be even better but food is easy to measure and essential I think. Also grocery shopping while hungry is disasterous.
Make sure your list is in order of the aisles. Or at least the sections. This makes it so much easier because you don't have to scan your list in crowded areas. You just have to grab the items in their predetermined order.
Also you're probably trying to do one big run to avoid having to go again and again which is respectable. But if you can talk yourself into it, a few smaller runs are much easier to get through in my opinion. I live near a grocery store rn and I go to get the ingredients or snacks that I need as I need them. I pick up 5-10 things and I'm in and out. The added bonus to this is that I can use a hand basket instead of a cart. I can slip around and past people. It's so freeing.
If it's possible to go to a different grocery store, it might be worth seeing if the vibes are better elsewhere.
Opposite to @BEE1000's rec, I'm also not a morning person. But I often go later at night. It's much quieter.
Noise canceling earbuds.
