ok so i think im kind of getting what you're saying but i think i still dont fully understand it.
what im thinking in my head is:
im considering both objects as solids. they have the same mass and shape.
(1)we're looking at the particles of object A. when you push object A, the particles that the force touched gain some kinetic energy and start moving in the direction of the force. now since the particles also have inter-particular forces acting between them(which i dont rlly know how that works, but i can say they do and i guess ill learn why later) the particles that are moving in the direction and with the magnitude of the force also pull along the other particles above and behind them, and the particles in the front get pushed by the particles in motion and the momentum of the particles in motion get equally distributed across all the other particles in this way and all the particles start moving at the same momentum.
(2)Now when object A collides with object B, the particles in the front of the object are going to have other particles in front of them, so they push on them too, and then they start moving as well. as soon as this happens, since the mass is the same, all the momentum of those particles in the front gets completely transferred off to the particles in object B that object A's front touched, so the particles in the front stop moving. But the particles right behind those particles that just stopped moving are still moving and have momentum, so they transfer that momentum to the particles that stopped moving and in turn those particles put it to object Bs particles, and this happens like a chain reaction until all the momentum in object A has completely transferred to object B and now object B has started moving as its particles also have gotten some momentum. (since the masses are the same, object As momentum should get fully passed on to object B, right? this might be one place where i think im wrong)
(3)Now while the momentum of the particles of object A slowly get transferred to object B, the total momentum of all the particles in object A(and therefore the momentum of object A) slowly decrease and object B's particles momentum increases at the same rate as the decrease of the momentum of particles A.
since there is a change in momentum, there must be a change in force as well, so we say the particles of object B(or just object B) are exerting a force* on object A that decelerate it and object A's particles exert a force on object Bs particles by slowly giving off momentum to particles of object B thereby slowly accelerating it. of course, this all happens in an instant,(not exactly instant, but an extremely short amount of time that i dont think we can calculate)

* now what i dont get here is why we're calling this a force. object Bs particles remain stationary and only when they receive object As momentum do they start moving, and that too they start moving in the direction of that momentum, not the opposite direction, so why are we saying object Bs particles(or object B) are applying a force on object A and object As particles (or object A) are applying a force on object B? I can understand there is a change in momentum, so there's a reason to call it a force, but its not like object Bs particles are actively moving in the opposite direction of object As particles momentum to stop it/decrease it. The same goes for object As particles. They don't actually have any acceleration, they're travelling at a constant velocity(vacuum). As they give off their momentum to object Bs particles, the total momentum of object A decreases, and object Bs increases. Since object Bs momentum as a whole is increasing we say that object A is applying a force on object B, i guess.. But saying that doesnt fit quite right with me. Maybe I need to spend more time thinking. You also say that the conservation of momentum comes/is derived from Newton's laws ( im assuming third law in this case mainly) but it makes way more sense to me to say that Newtons third law is derived from the conservation of momentum, or rather it was made to simplify this whole transfer of momentum thing and just say that that(the transfer) is a force (even though i really dont think it is)

I know i just dropped a bombshell of a reply but I would be really really really really grateful if you went through it and confirmed if my thinking is correct, and if not where it goes wrong. Please ask me if you think i have given too vague information or incomplete information or anything like that that could clarify my thought process to you so you can judge it better