Applying for a faculty job without history of external grants
While having a history of external grants is helpful, it is not mandatory. I was in a similar position as you were, and managed to secure several offers. What you need to do is have good answers prepared for these two things:

Why Not?: In my case, as with yours, I was in a research institute, which meant things were supported by large grants that were well beyond my "pay grade" to pursue, and where the priorities for postdocs were producing research and doing the things that kept funders happy, rather than chasing new funding. People were very understanding of these sorts of positions.

How Will This Change?: Given you don't have a track record of getting external funding, you need to be able to articulate how you will go about getting one. Having a clear idea of what mechanisms you'll target, how you'll frame your research that way, etc.

Basically, you need to frame not having grants as a deliberate, strategic choice in your old position that will change in your new one as you become an independent researcher.