Can you summon during regular battles in Final Fantasy VII Remake?

You can summon in regular battles too, it's not just the boss fights.

In order to start the summon gauge you usually need to either get a character to low health (in the red), or stagger an enemy. Once either of those criteria is met the gauge will start filling.

However, there are some situations where certain summons are not available. Based on my experience and research, summons are only available if the battle area you are fighting in is big enough for them to fit in and move around in.

So there will definitely be some battles in tight areas where summons won't fit, so can't be called. The smaller the summon in size, the more likely you will be able to use them.