No, when he shot the police officer on the street. JD Tippet, just 40 minutes after JFK was shot. He didn't shoot anyone in the theater, afaik.
He seems to have dropped the shell casings at that scene, so he did have his pistol at the theater? But he never shot anyone there.
There's also speculation that Oswald was inside the theater already when Tippet was shot... or arrived there minutes later when it was a long walk away :/
really long article, full of questionable stuff they explore ALL the possible theories regarding Tippet's shooting.
Best take-aways:

• Tippet was shot 4 times with 2 kinds of bullets (both could be from the same revolver though ) and Oswald took the time to remove them and leave them at the scene, along with other identifying materials.
• Oswald had 2 dollar bills that had been ripped in half. He only had half of each. A common way to identify a contact, yes? They have the other half, it's impossible to fake it.
• eyewitness testimonies were all over the place, but 2 did say there were 2 men present when Tippet was shot.

Also: the Dallas police force received (iirc) 300+ 'tips' on Oswald's location, but for the tips from a shoemaker and a theater worker they sent a LOT of men to a single theater. This would support the idea that Oswald was trying to contact his 'handler' as theaters were VERY often used as contact points back then. Possibly still are?
Iirc they had leaflets out with Oswald's picture on them & distributed within an hour? in under 30 minutes. Rather remarkable since there were no Kinkos back then.

I could be mistaken, but the endless parade of "questionable facts" in the Official Story are just too much to overlook. That and the history of all governments to lie to their own people with impunity.
Anyhow, it's always interesting to discuss and research the subject. I learned a bunch just now :>