Q:

Is "assume a noun" possible, instead of assume that~?

The verb to assume is followed by a clause or to infinitive.
Though dictionaries don't mention it, for me, it seems correct to use this structure: assume + a noun. For example:

Assume a sudden increase in population, ~

Is such a structure appropriate, or should it be written in the clause?

A:

When a noun is the direct object of the verb assume, most of the time the connotation of the verb is undertaking some role or task:

When the owner of the company died, he assumed the powers of CEO.

But for the meaning of assume as "take as true," a noun can serve as direct object:

I think it's a racism thing when you assume things about Ed.  

This is common in mathematics:

If we assume the Riemann Hypothesis, the real part of ρ is always 1/2.  

