Could Democrats have reduced undoc immigration during the Biden years without the proposed additional 20 billion?

It seemed to me Democrats wanted to do things by the book - hire more judges for asylum courts for example. Was there more that could have been done with the available funding to reduce the numbers but stopping short of slamming day laborers and car washers to the pavement by masked unidentified federal agents?

Democrats have raised the point that Biden proposed more funding to fix our broken immigration system. But that was shot down at the behest of Trump. But to my eye that proposal came too late and even reluctantly. Of course the irony is now Trump is spending 10 times that amount on the ICE secret police with less efficient results but extra violence.