The topic at hand requires both parties to have a proper understanding of basic physics, including the fact that there are more forces that exist than just pushing. You don't have that, so how can we proceed on the topic at hand?

Can an object be pulled by another object if the leading object itself is not pushed?

Yes. Magnetic force is a great example of this.

(think mechanically for now)

If you want to talk strictly mechanics, as in mechanisms, then a scenario such as a winch pulling in a load would be the load being pulled via a rotational method, no pushing of the leading object.

A very simple version through mechanics (of movement) though can just be you picking up your cup of coffee and bringing it to your lips. You're pulling it inward.

The topic at hand requires both parties to have a proper understanding of basic physics, including the fact that there are more forces that exist than just pushing. You don't have that, so how can we proceed on the topic at hand?

Can an object be pulled by another object if the leading object itself is not pushed?

Yes. Magnetic force is a great example of this.

(think mechanically for now)

If you want to talk strictly mechanics, then a scenario such as a winch pulling in a load would be the load being pulled via a rotational method, no pushing of the leading object.

A very simple version though can just be you picking up your cup of coffee and bringing it to your lips. You're pulling it inward.