OK you will need to bypass the amp and because the amp has electronic crossovers for the speakers it is not a simple matter to connect your headunit directly to the speakers without some sort of crossover. You could use a simple capacitor crossover to do that, with unknown results. My feeling is that unless you know a lot about car audio, then you are better off looking for a solution that may cost a little more, but would work. You options are:
1/Replace the factory door speakers and wire the headunit directly to them using the crossover provided/integral with the new speakers.
2/Keep the existing speakers but connect the headunit low level outputs to an electronic crossover and seperate amplifier.
3/Keep the existing speakers and wire a crossover (in each door) to the woofer and tweeter, such as:
https://www.ebay.com/itm/2-Audiopip...917287?hash=item2a23c7b627:g:fOQAAOSwEOpaAkAg
Option 1 would be the simplest/best sounding route. You could add a sub and sub amp with either option.
I would look for a shallow mount 6 1/2" speaker with integral tweeter for the front doors, such as:
https://www.woofersetc.com/focal-icu-165-6-5-70w-rms-2-way-coaxial-car-speakers.html.
You could probably retain the rear door speakers and use a crossover as I have suggested.
It really depends on how much you are willing to spend. In any case, you will need to identify the correct wiring from the original amp to the speakers. It may be easiest to remove front and rear door door cards (ie inside) to allow access to the speaker wiring. As I suggested previously, you can use a signal tracer to identify each wire. Alternatively, it may be easier/ cheaper to expose the speakers but get an auto electrician/car stereo shop to identify the speaker wires for you. You can then do the rest of the install yourself. You will need to run wires from the headunit to the speaker wires from the original head unit. Once you have one set of two wires (going to each door) you can install the crossovers in each door, and wire the tweeter and woofer to the crossover.
Unfortunately it is a lot of work and if you can do at least some of it you may be better off getting an auto electrician etc to do part of it. Given that the headunit is not working, I would pull the fuse for that until you have the speaker wiring sorted.