The client offers full time but no H-1B. Don't take that job offer. There is no future there anyways and it is weird that don't offer immigration support. Who they expect to find? Like hire someone for 1-2year and let them go. They will realize soon anyways just turn down the offer stating your long term concern.

Just stick to the consultancy with H-1B and then move to a new firm since H-1B transfer is really easy. Note that getting picked in the lottery is a super big deal and it is pure luck these day. Also, getting a full time job at a nice firm that offers H-1B is not difficult, I mean there are literally thousands of companies that offer both :)