Singleton service creating an object that requires a scoped service

Hi all;
I'm getting a scope error on this:
I use AddDbContextFactory()
to get a factory that I then use to get a DbContext. The factory is singleton scoped.
The DbContext constructor requires a service. The required service has session scope (it must). The factory is creating this DbContext.
The DbContext created will have a very short lifespan, and be disposed before the session ends. But the factory does not know that.
In this case, is this a scope exception? That the singleton factory will not allow the DbContext it creates to have a session scoped service in its constructor?
And if so, is there any way around this? I think I can make the DbContextFactory session scoped - but is that a good idea?
Is there a way to load the service other than as a constructor parameter?
The way my code is written, the created DbContext will always have a lifespan within the session scope.
thanks - dave