Is there anything I can do to move a claim forward?

I’m new to US insurance system and looking for some advice. I’m also new to this sub so apologies in advance if I wasn’t clear or used a wrong term.

I did a NiPt and carrier screening with Labcorp back in June. Both tests have doctor’s order. As of today I still haven’t received a bill for the tests. I called Labcorp today and the representative told me “medical records for the service of the day need to be sent to insurance company”. When I asked him what that means, he suggested that I contact my insurance company. I then contacted my insurance company. Insurance said this claim is pending on the provider (Labcorp) to submit medical records/medical necessity. And the provider has been sent the EOB that indicates this. I then contacted Labcorp again. Got to a different representative this time and she kept saying that this is pending insurance and I will get a bill.

The claim seems stuck somewhere. Insurance says it’s pending on Labcorp and Labcorp says they are waiting for insurance. I feel like I’m in a loop. I just wanted to pay the bill to close this case but I can’t get a bill just yet.. Is there anything I can do to move this claim forward, or should I just let the two companies figure it out and see what happens?