Can I use Flash of Genius on an initiative roll?

The Artificer’s Flash of Genius says:

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.

On the one hand, an initiative roll is an ability check, which means that it’s eligible for Flash of Genius. However, it’s not clear whether I would have my reaction available as initiative is being rolled. So, can I use Flash of Genius to add to an initiative roll? Does it make a difference if I’m surprised?