Simon Cowell stepped out in NYC with his 6-day-old son Eric for a baby checkup on Thursday, Feb. 20 -- see the picture Credit: Abaca USA/AKM-GSI; Brian Prahl/Splash News (inset)

Proud pop! Simon Cowell has quickly become a doting, hands-on dad, as the British star was photographed with his newborn son Eric in NYC on Thursday, Feb. 20.

The 54-year-old first-time dad held on to his boy's car seat as they left the doctor's office on the Upper East Side in Manhattan. Cowell donned a black peacoat and matching sunglasses as Eric was bundled up in an adorable white blanket and hat. Cowell similarly took charge on Feb. 16, as he and girlfriend Lauren Silverman left the hospital with their boy in tow.

The former X Factor judge and Silverman, 36, welcomed their little tyke on Feb 14, and shared the first photos of the baby boy via Twitter soon after.

"Mum, Dad and Eric. Now two days old," Cowell captioned on Feb. 16, with a photo of himself, Silverman, and Eric sitting on a hospital bed. "I never knew how much love and pride I would feel."

He added of his dogs Sqiddly and Diddly: "The last three days have been incredible. Eric Lauren sqiddly and diddly all happy."

Eric was named after the star's late father, who died at the age of 81 in 1999 of a heart attack.