If your body control module (BCM) has the RF receiver then you can just buy the fobs and have it programmed. Without crawling under your dash and looking, if you have a shop that's friendly and near by that has a Snap On or Autel or a similar scanner they can just plug into it and hit program remotes and if it sits there and waits for you to press the button on the remote then your car will take a remote but if it says you can't then it means your BCM doesn't have that option. You can buy inexpensive after market fobs, I have had some that work and a few that don't.
Funny you should mention this as I was cleaning up the other day and still have my key fob from a 2018 that I traded in 2 years ago. The dealer that I traded it in to wouldn't give me a 2nd keyfob for the 2020 that I bought (claimed it was a new policy) so I told them that I wouldn't be giving them the 2nd keyfob of the trade-in. Apparently they didn't bother to get the 2nd keyfob from me. This one is a smart keyfob. I suspect the one you need is different, if it's not the Exclaim! or similar trim. I'm contemplating putting this keyfob on Ebay as they run about $80 new.
The OP stated she has a base model, but did not specify with MT or AT. As stated, base models had the option of keyless entry; otherwise they were equipped with:
Here is a list of standard & optional Comfort, Convenience & Security equipment:
I need to get a fob from ebay or the like. I really don't want to pay the $160 the dealer quoted me for it. I had a second key made at the automated kiosk for $25 but it's just the normal key not the flip one with the fob. I have a fob for the gen 1 Soul from a 2011. It won't work for me but if anyone needs it let me know.
I am not sure if the OP ever mentioned what trim line her Soul has--I was only able to see "2019 4 Door 4Cyl/FWD". I think all of the Souls have 4 doors, 4 cylinder engines, and are front wheel drive. Did she purchase the Soul from a dealer or a private party? Most of the 2nd generation Souls do not have immobilizer chips in the keys and can be started with the non-transponder keys like SmoovC posted--there is a possibility that the OPs vehicle is not a base model but was sold with a simple key.
Would be helpful if the OP could post the trim level (base, plus, exclaim) as well as a photo of the actual key (the cut pattern should be blurred out if desired).