There will be a wire in the original connector that gets turned on when the radio is on. That is for the amp and / or power antenna. Your new radio will have that same wire in its harness. It is typically blue or yellow. I can't remember for sure because I don't repair aftermarket radios. If you connect those wires together, the amp will turn on and you should get plenty of sound, but you'll need to bypass the amp to make it sound right. Only Chrysler radios all run speakers directly AND they can be used with their amps because those do not change volume or power. They only modify the tone response for the shape of the vehicle. Ford and GM do that by having a multitude of different radio model numbers. When their radios use an amp, they NEED an amp to get the necessary volume.
If you use the speaker outputs from your new radio and run them through the amp, the sound will be way too high and distorted. If your radio has line outputs, you can try connecting those to the truck's speaker wires that go to the amp. If you don't get enough volume that way for comfortable listening, you'll need to bypass the amp and use the radio's speaker output wires.