You can take reactions outside of combat.

As evidence of being able to take a reaction in response to a relevant trigger outside of combat, consider the spell feather fall:

Choose up to five falling creatures within range. A falling creature's rate of descent slows to 60 feet per round until the spell ends. If the creature lands before the spell ends, it takes no falling damage and can land on its feet, and the spell ends for that creature.

Feather fall has a casting time of 1 Reaction,

which you take when you or a creature within 60 feet of you falls.

I think it quite obvious that the act of falling does not initiate combat or require rolling initiative, and so there is a clear sense in which feather fall is intended to be usable outside of combat. Therefore, you have your reaction available outside of combat.

Flash of Genius works if you are not surprised.

In the order of combat section of the Player's Handbook, determining surprise comes before rolling initiative. Surprise is the only thing that would prevent you from taking your reaction at this point:

The DM determines who might be surprised. [...]

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 ends. A member of a group can be surprised even if the other members aren't.

It is in the section following the surprise rules that the rules for initiative are explained. After determining surprise comes the ability check for initiative:

When combat starts, every participant makes a Dexterity check to determine their place in the initiative order.

This is the reaction trigger:

When you or another creature you can see within 30 feet of you makes an ability check or a saving throw, you can use your reaction to add your Intelligence modifier to the roll.

You are making an ability check when you roll initiative¹, so as long as you are not surprised, you may use your reaction at this point to use Flash of Genius.

¹ To further solidify this particular point, the Sage Advice Compendium clarifies that the Bard's Jack of All Trades feature adds half-proficiency to initiative roles: "Don’t forget that initiative rolls are Dexterity checks, so Jack of All Trades can benefit a bard’s initiative".