You can make a selection of contacts in some other system and trigger a campaign for these contacts only. If so, you must switch starter type under the conditions for your campaign by clicking Switch to API.
Learn about the technical setup on ApiDocs.
By changing your starter to be triggered with an API call, your first step will automatically get unscheduled (and executed when you call the campaign).
Depending on the nature of your campaign, you can set a scheduled time on your first step by clicking in the bottom of the step.
You can also clear the scheduling of a step to instead be executed when the campaign is triggered. Just make sure that API triggered steps (unscheduled) are not placed after a scheduled step (all triggered steps must be placed together and in the start of your campaign).