Is there a word/idiom for feigning a belief for the purpose of constructing an argument?

"For argument's sake" is, in my experience, a common idiom and, in fact, has been used as the title of at least one book.

A slight variation is "For the sake of argument" which was addressed in xkcd #1432 (see an explanation here). The title text on the image states in part:

...it's a DEVICE for EXPLORING a PLAUSIBLE REALITY that's not the one we're in, to gain a broader understanding about it.

Additionaly, the Oxford Dictionary offers the following definition for the later (but does not list the former):

As a basis for discussion or reasoning.

According to Google Ngrams, the latter seems to be more common.

The aforementioned comic also makes mention of "playing devil's advocate".

Let me additionally suggest the term "arguendo": https://en.wikipedia.org/wiki/Arguendo.

You can also simply start your sentence with "Assuming...".

Google Ngram for "arguendo":

I commonly hear it put as playing the devil's advocate.

In common parlance, a devil's advocate is someone who, given a certain argument, takes a position they do not necessarily agree with (or simply an alternative position from the accepted norm), for the sake of debate or to explore the thought further.

Devils Advocate Wikipedia article

Google Ngrams seem to also be popular, so here's one.

Consider, premising.

PREMISE

: (used with object) to assume, either explicitly or implicitly, (a proposition) as a premise for a conclusion.

: (used without object) to state or assume a premise. Random House