Seems like you can

https://origamiusa.org/thefold/article/diagrams-one-cut-hept...

The one cut is to remove the perimeter of the square that lies outside the heptagon. Without the cut, you could make a crease, and fold the excess behind the heptagon.

My reading is that it's a convenient near-7 approximation someone developed, like using 22/7 for pi.

Certainly good enough for practical handheld construction purposes, but not geometric-proof-y stuff.

Checkout

    Scimemi, Draw of a regular
    heptagon by folding.
    Proceedings of the 1st
    International Meeting of
    Origami Science and 
    Technology. 1989

Simultaneous folding is mathematically a strictly more powerful primitive.

Are you familiar with Lill's method of finding real roots of polynomials of any degree ? Simultaneous folds are a realization of the same idea

https://en.m.wikipedia.org/wiki/Lill%27s_method#Finding_root...

Yes.

But remember one is dealing with idealized / axiomatized folding. The situation is similar with compass and straight edge geometry -- those physical lines and circles marked on paper are approximate but mathematically, in the world of axioms we assume the tools are capable of perfect constructions.

This paper discusses constructing heptagons, with some history and the maths.

http://origametry.net/papers/heptagon.pdf

It shows both a single sheet and a modular version.