"A party"

[Rachel Adams]

If I am mentioning it for the first time can I use an indefinite article before "party"?

"I met her at a party."

 

[Rover_KE]

Yes.

(There was no need for quotes in the title.)

 

[emsr2d2]

If I am mentioning it for the first time, can I use an indefinite article before "party"?

"I met her at a party."

It's not just that you can use "a". You must. The sentence would be incorrect with no article and, if the specific party hasn't been mentioned before or the listener doesn't already know what party you attended, "the" would be wrong.