I would just say "we are being pushed by big companies" though I think your sentence is technically correct. For "pushed forward" you might say "there's been a big push forward in cancer research in the last few years" or "the government is pushing us forward towards a sustainable future" or something like that. I think "pushed forward" carries the implication that we are going towards something better.

Try rewording with 'persuade'.

It makes sense, but certainly not normal speach, I think the "forward" will have been droped into the sentence by some idiot copywriter.