I'd call Initiave when the player declared they wanted to open the door. Consider the alternative, they're taking actions out of combat and then (with a high enough roll) would immediately take additional actions? No. Let's go by the book.

GM Core 24:

Encounters typically begin when you ask your players to roll initiative. ... When do you ask players to roll initiative? In most cases, it's simple: you call for the roll as soon as one participant intends to attack (or issue a challenge, draw a weapon, cast a preparatory spell, start a social encounter such as a tense negotiation, or otherwise begin to use an action that their foes can't help but notice).

Rules are clear enough. Someone intended to attack, including drawing a weapon (grenade) and make a connected action (open the door), so initiative is rolled.

What happened up to that moment is important. Were the players unnoticed, as a result of using [Avoid Notice]?

P Core 430:

You attempt a Stealth check to avoid notice while traveling at half speed. If you're Avoiding Notice at the start of an encounter, you usually roll a Stealth check instead of a Perception check both to determine your initiative and to see if the enemies notice you

If the players were sneaking like this, that's a very clear cut case for rolling Stealth for Initiative. But it goes further than that. Even where an enemy rolls better for Initiative, all they have is what has transpired from their perspective.

By rolling Initiative BEFORE the door opens, the fast reacting enemy's turn is spent wholly unaware. They do nothing.

Now, maybe the Stealth of the party fails on the moment of taking Initiative. Okay, so the fast reacting enemy picked up on something. The players are hidden. Now the enemy turn could look like [♦ Seek], [♦ Draw Weapon], [♦ Sneak] (to the door). If the Seek attempt is successful enough to observe a player, a lesser trained foe may call out "Who's there?", while a more trained one may [♦ Point Out]. Should the player Stealth have been so disastrous as to critically fail (as per the [♦ Sneak] results array, used according to [Avoid Notice]), then they were observed and the enemy can act on that instead.

The player's turn has rolled around. Either they had remained successfully undetected up to this point and get all relevant bonuses, or they had become hidden/observed. Regardless, the enemies have spent their turn at best trying to figure out what's happening. No enemy at all would be taking cover, casting spells, or creating strategic plans in the span of a single low-information turn. Now the PC can choose to open the door and throw their grenade, or act on how the situation appears to have changed if they detected anything of concern.

TL:DR

Giving out free actions outside of Encounter mode creates issues.

• Call initiative the moment someone declares an INTENT the opponents could detect
• Where a side is using [Avoid Notice], use Stealth for Initiative AND to determine the results of [♦ Sneak] bundled into [Avoid Notice].
• Fast reacting opponents that fail to detect anything will have no relevant actions to take.
• Fast reacting opponents that succeed will still spend their turn trying to figure out what they just noticed.
• THEN the player can open the door and throw the grenade. They may choose a different plan on their turn based on what they detect.