Brother it is a long and hard road ahead.
There is a red flag that I want to address but first to answer your question-
You can incorporate but cannot work for the company at all (even for free).
You cannot get paid from that incorporated company in any form (even if it is house rent).
Some people choose to incorporate in Hong Kong /India and find RELIABLE partners in India and US to run the business. If you are writing code .. outsource to developers in India or let a team in India do it. (It is hard to keep track of whether you wrote any code for it or not, so you would need to come up with a system to document such activities.)
If you need to give up equity, give equity either in the HK/Indian company or create a separate company in US which own's majority equity stake in the HK/Indian company. Then you can issue equity in the US company(which is only a stake holder, doesn't actually do business).
Now the big red flag....
The advisor is worth nothing.
I learnt it a little bit hard way and I don't want to go on and on with examples and anecdotes so I will keep it simple.
1) Help out for free. Do not ask for money or equity
2) Look at the product, give feedback as well as do other introductions if they are excited about the product.
3) Invest !! They get equity only if they invest. You can generally defer the valuation discussion by using convertible notes or SAFE (check out YC) with some discount (at least 20%)
Trust me, right now you are excited to get some attention from this advisor but unless she invests, her excitement will subside way before yours does and you will be left frustrated. If she doesn't invest, she doesn't believe in either the idea or the team. She will perform way below your expectation.
Move on and find some other advisor who is willing to invest.
If you cannot find even a single industry expert who is willing to invest, thats sufficient validation for you that your idea or team sucks. Pivot to the next idea you are excited about!
Sorry for not sugar coating in interest of brevity