Well, this is mid summer, after Poles already made moves to free up cash. In order to do so, he had to jettison many vets. At that point, he had cap space and more roster spots unfilled with actual NFL players. The cap space $ includes 51 players, but that's after starters and contributors from 2021 were gone and not replaced.
July 6th after June 1 cuts and after trades tells where he got to, not where he started.
He had moved Mack, Hicks was gone, Goldman gone, Foles, Trevathan, Cohen, etc. All those people were under contract when FA started.
He allotted some to Ogunjobi and that didn't work out. That did cost them an opportunity to pursue others in the meantime.
But, no, when he took over the Bears were not flush with cash with a roster full of talent. Their space later was due to creating roster holes.
I don't have a list of top FA's that signed after July 6th, but I am guessing it is pretty short.
And FA's don't accept the same $ to go to a noncontender, so his choice at that point is to overpay. He obviously made the choice - wisely - to not overpay and commit to higher salaries a year (at least) before the Bears could attract real talent at the right price.