Can you put a counter on a permanent with a triggered ability before that permanent's own enter-the-battlefield trigger resolves?

When a permanent enters the battlefield, all triggered abilities that trigger from that event are placed on the stack together before any player receives priority (CR 603.2, 603.6b). The active player orders their own triggers, then the non-active player orders theirs — all on top of the stack simultaneously. This means no trigger resolves until a player receives priority and passes it.

Because all ETB triggers from the same event are placed on the stack at the same time, you cannot use one ETB trigger to affect another ETB trigger's resolution order in the same batch — they all go on the stack, and then resolve one at a time from the top down. So a permanent's own ETB trigger and another triggered ability generated at the same time are both pending simultaneously on the stack.

However, it is entirely possible for an opponent's or another permanent's separately triggered ability (or even a different trigger from the same event ordered above the first) to place a counter on a permanent before that permanent's own ETB trigger resolves. The permanent exists on the battlefield the moment it enters, so it can legally receive counters at any time, even before its own ETB trigger resolves.

Concrete example: You control Hardened Scales and cast Luminarch Aspirant. Both 'enters the battlefield' triggers fire: Hardened Scales triggers to add an extra counter, and Luminarch Aspirant's own ETB trigger puts a +1/+1 counter on a creature. You stack them so Hardened Scales resolves first, placing a bonus counter on a creature, before Luminarch Aspirant's own trigger resolves. If instead you wanted a counter on Luminarch Aspirant itself before its own trigger resolves, an opponent's simultaneous ETB trigger ordered above it could accomplish this.

The key rule is CR 603.6b: triggered abilities from the same event are all put on the stack before any resolve, and their relative order is chosen by the players controlling them. A permanent can receive counters before its own ETB trigger resolves as long as another trigger or effect that resolves first places them there.