Just don't sign anything that says you'll get paid when they get paid.
If you have not worked with the agency before or if you don't trust them, then work only as a W2 to the agency, not a 1099 or C2C. They can't screw with a W2's pay regardless of whether they get paid by the client. Too many potential Fed and State legal problems.
Read the entire contract. While they can't link your pay to when the client pays, they can link it to the clients approval. I got screwed by this once.
The job was a W2 assignment but the contract clearly stated that the client must sign my time sheet before I get paid. I worked the hours but even the state said that they couldn't enforce payment without a signature. The client didn't dispute my hours, the work, nothing. They just didn't want to pay me anymore. They were treating my work like some kind of fixed bid project. They wanted me to finish it but no more pay.
The state said the client disputed nothing and per the contract, there was nothing they could do to get my pay.
So ask the agency what happens if you work the hours but they don't sign the time sheet?
Also request for a backup "authorized signer" for your time sheets. Some managers are so busy, out of the office or on vacation that getting paid can be an issue. I had one assignment where the guy was out so much that my pay was a month behind. Once again, another broker treating that signed time sheet as client authorization to be invoiced for your worked hours. Note it's not tied to when the client pays the bill but to when the client authorizes or approves the hours worked.
I've never seen anything so crazy. For 10 years prior to first seeing this, we didn't care about signed time sheets since the contract "authorized" the work but I guess that's the difference between being a consultant and a contractor.