If you're struggling with affordability you can see if at high school or university students are offering tuition at lower rates - I've been teaching as a side gig since my uni days (10+ years ago), initially at around £15/hr and now at £30/hr (I now do it as a hobby and a way to maintain my skills).
I've taught up to Grade 8 ABRSM (students gaining merits and distinction), having gained diplomas in piano and violin when I was at school.
Where it becomes more important to get a professional (conservatoire grad / professional performer ) teacher is if 1) your child shows aptitude and willingness to do music professionally or 2) around grade 4/5 where technique and musical interpretation become more of a concern.
If your intention is to enable your kid to become a professional, then it's worth going with a pricey and experienced teacher who has a string of successful students who have been able to get into great music schools from lesson 1. Because it'll save time on correcting technique down the line.
Else, if the intention is just getting the kid to enjoy learning and playing music, then realistically, a uni student who has reached diploma level and is able to be engaging and reflective is able to get your kid started with music.
I had about 12 teachers growing up, all very talented performers. Only 3 were decent teachers and about half actively horrible (clearly resented having to teach) , so that's shaped my viewpoint.