Disclaimer: I do not know anything about FastAPI framework(python) or uvicorn(ASGI server).
I do have experience with using IIS as a front end for Tomcat. This involved installing an ISAPI filter into IIS (listening on HTTP and HTTPS) and configuring it to do port forwarding to whatever port we had Tomcat listening on. Client<-->IIS<-->Tomcat<-->WhateverDatabaseItUsed
I don't know if that's what you mean by "deploy ASGI server on top of IIS". You might have better luck asking this question in an ASGI forum or searching their documentation for ISAPI filters.
Maybe this? https://github.com/mjkillough/iis-asgi-handler
If you just want to run a program at system startup, you can use the Windows task scheduler or a tool like NSSM that runs command line programs as a service.