You can use a reaction to affect initiative rolls.
Initiative (PHB 177):
At the beginning of every combat, you roll initiative by making a
You would automatically become part of the combat, but there is not a single instance, in the rules, that necessitates that you can't start the combat with a reaction with the usual exception of Surprise (PHB 189):
If you’re surprised, you can’t move or take an action on your first
turn of the combat, and you can’t take a reaction until that turn
Reactions (PHB 190):
Certain special abilities, spells, and situations allow you to take a
special action called a reaction. A reaction is an instant response to
a trigger of some kind, which can occur on your turn or on someone
If you worded the trigger correctly, you would intervene in the combat and therefore would have to roll initiative.
Initiative (PHB 189):
When combat starts, every participant makes a Dexterity check to
determine their place in the initiative order.
You couldn't take another reaction before it is your turn.
When you take a reaction, you can’t take another one until the start
of your next turn. If the reaction interrupts another creature’s turn,
that creature can continue its turn right after the reaction.