Can I turn on do not disturb without setting a schedule?

ktwk ~ Yes, here are a couple of ways:

Say: "Hey Siri, Turn do not disturb on."

And: "Hey Siri, Turn do not disturb off."

Also, Control Center requires FIVE actions (swipes/taps) to change Do Not Disturb mode. But with a simple custom shortcut on your Home screen, you can reduce it to just ONE tap to toggle the mode On/Off. If you're interested, choose one of the icons shown below and a name for the icon, and I'll send you the iCloud link:

And here's the simple shortcut which hides behind those icons:

Shortcuts User Guide for iPhone and iPad

Shortcuts User Guide for Mac

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Yes. You can turn any of your focus modes on or off manually in control center.