Idiom or word to say to someone who is talking without proof or data

Sounds like the contractor served up a nothingburger. From Lexico:

nothingburger: Something that is or turns out to be insignificant or lacking in substance.

A related possibility is Where's the beef? From Wikipedia:

Where's the beef? is a catchphrase in the United States and Canada, introduced as a slogan for the fast food chain Wendy's in 1984. Since then it has become an all-purpose phrase questioning the substance of an idea, event, or product. [Emphasis mine]

You could say the contractor's recommendations are pulled from a hat, like how a raffle winner might be selected - the recommendation has no rational basis or support, and is seemingly random.

One could also say the contractor is talking out of their ass, which occurs when a person expounds upon a subject with seeming authority, although they don't actually know what they're talking about. Another common term for this is bullshitting.

A way to express the utter uselessness of the recommendation is to remark "that and fifty cents will buy you a cup of coffee". Assuming a cup of coffee costs 50 cents (although not genreally true these days), the suggestion carries no value whatsoever.

This idiom might leave the consultant fuming afterward but you could say that he's "talking through his hat".