How to get the time of impact for two objects moving in different directions?

First of all, I can´t use Unity´s physics system. Then I have an object on the wall and one on the ground. Both move in different directions and a rigidbody might get stuck in between. I want to simulate a collision if that happens, so I need to get the time of impact if it´s being pressed from opposite sides. Assuming is static, the objects should push it until they collide. I can move the rigidbody based on the first collider´s direction, so basically I need to see which object collides first (in case is hanging in the air, else is the platform it is standing) and see if there´s a second collision from the opposite side, which I get from the time of impact. But I don´t know the time of impact, I only know the initial and end positions of the three objects.

I recommend using the OnCollisionEnter. This method gets called when your rigidbody first makes contact with a collider. There are other methods that you could also make use of: OnCollisionEnter, OnCollisionStay, & OnCollisionExit. When it enters you could set the time of impact.