Alec Baldwin just filed his first official response to the new charges being brought against him in the "Rust" case in New Mexico -- and the first thing out of his mouth is ... hurry up!

According to new legal docs, obtained by TMZ, the actor has been ordered to appear before a judge in NM to answer to the involuntary manslaughter charge being filed against him (again) ... and he's gotta do so on Feb. 1 at 11 AM through an official plea.

The paperwork notes that AB can show up to court via phone or video conference -- but he's gotta let the judge know one way or the other ... guilty or not guilty. Based on the last time this happened, something tells us Alec's gonna go with the latter.

In fact, his attorneys filed a response to this almost immediately -- submitting documents that make clear ... he wants to get this over and done with, stressing his constitutional right to a speedy trial.

One of the reasons his legal team cites as wanting to get the show on the road here is because it'll "minimize public vilification and suspicion." Plus, he wants to "avoid the hazards of proving his innocence that often arise after a lengthy delay in prosecution."

Remember, Alec was slapped with new charges last week -- namely, involuntary manslaughter through negligent use of a firearm, or in the alternative ... involuntary manslaughter without due caution or circumspection. Before the charges were dropped the first time, he was facing something very similar ... and the entire time, he vehemently denied any wrongdoing.

Of course, this all has to do with the fact that Alec was using the prop gun on set -- which somehow fired and sent a live bullet through the late Halyna Hutchins, who was the DP.

Alec had chalked it up to a horrific accident -- but prosecutors there in New Mexico have alleged criminality was afoot, and they've been gunning for Baldwin for a while now. His first official reaction to them going after him again basically boils down to ... c'mon, let's go!