I can't think of an example of where the answer given - 'the construction hardly starts' - is used in American English.

Perhaps 'the construction has hardly started' would be a better translation.

Maybe, "The construction is barely beginning"? This sentence is awkward in US English

"The construction is just beginning" was accepted.

"The construction has barely started" sounds natural to me. Anyone else?

I believe The construction is scarcely beginning is OK also. I agree with respreng!

I put "The construction is just commencing" and it was flagged wrong.

In english could we simply say "construction is just starting'. i.e. "The" is unnecessary

the construction just started is correct, no?

I would say "the construction just started" in English.