A larger Soviet fleet changes NATO's problem

Would a larger Soviet surface fleet have pushed NATO toward more submarines, mines, and sea denial?

Yes, but NATO would still need to find Soviet forces already deployed from forward bases rather than merely seal Soviet waters.

Mines, submarines, and torpedoes can form a barrier, but they cannot solve the problem once an enemy fleet has forward-deployed. Soviet supply facilities in places such as Cuba or African states would create a wider search and targeting problem. The key distinction is between blocking an exit and coping with a navy already present around the world.