I usually log in to a Stack Exchange site using another site (Google, Facebook, etc.) as my account provider. However, I'm currently in an environment where my login provider is blocked. Is there any way for me to log in to my existing Stack Exchange account even though I can't use my account provider?
Yes, you can use standard email and password login, and associate that to your account by following: How do I change my login provider(s)?.
If you use the same email address while registering, account association may happen automatically, so you don't even have to worry about that step if that happens. In some cases (such as you being a member of a Stack Overflow for Teams site, or if the system couldn't verify something), it may create a second account; if that happens, request that your accounts be merged.