Trump co-hosted a Spaces on X interview and he's talking about a wide range of topics, including Sunday's foiled would-be assassination attempt. He says a witness saw the suspect running to his car and snapped photos of him, his car and his license plate and fed it to cops, helping them track the guy down.

As we reported ... Trump was golfing Sunday morning at his club in West Palm Beach when the Secret Service noticed a rifle sticking out of some bushes and opened fire.

Law enforcement says the suspect, Ryan Wesley Routh, had posted up for about 12 hours in a makeshift sniper tent about 400 yards away from the Republican nominee ... and took off running when he was sniffed out and fired upon.

Trump says the civilian witness, a woman, noticed him and "did a phenomenal job" taking pics.

DT says ... "How many people would have the brainpower to follow him to the back of his truck?" He says the key piece here was the photo of the guy's license.

Routh left behind a loaded SKS-style rifle with a scope, two bags and a GoPro camera ... according to the authorities. The gun has since been taken by police as evidence.

He was later pulled over by Martin County Sheriff's deputies ... where he calmly lifted his shirt over his head, walked backward towards the deputies on the scene and surrendered himself to be put in handcuffs.

Trump says once authorities had the license photo from the witness they were able to use some high tech to find the guy ASAP.

Routh made his first appearance in a Florida court Monday, where he was charged with possession of a firearm by a convicted felon and possession of a firearm with an obliterated serial number.

He remains in custody, and will be until his arraignment on Sept. 30 ... however, he'll be back in court before then for a formal detention hearing. More charges are expected.

Trump survived a prior attempt on his life in July, when Thomas Matthew Crooks squeezed off shots at DT's rally in Butler, Pennsylvania.