Hello!
From what I've seen so far in the game, not many low level players like to engage in PvP.
This is a very curious phenomenon to me because, it is like they are playing an online single player game... but that's just my two cents.
In any case, it's sometimes kinda hard to challenge players while they are walking (you have to click on them and then select battle). Not only that, but you don't get anything for these battles! This is one of the main reasons I think people skip low level fighting. Maybe giving "PvP money" to these people so they can buy aesthetic items(hats, clothes etc?), berries, potions, you know, small things? I think any small reward would drastically increase the poké battles at early game...
Also, there should be a way to put a status over you head like "Looking for battle!", so people passing by would click you and accept the challenge instead of you having to try to find someone yourself.
Furthermore, the possibility of creating a private chat bubble over you head like "Looking to trade!/Looking for battle!" would really make it simplier IMO, so that anyone interested in what you wrote in your chat title, would be able to just click the dialog box over your head and enter your room!