The two new parents are doing well and peaceful as they and baby boy Eric spend time in the U.K., a source tells E! News. "They baby's doing well, he's very strong. He can already hold his head up! He's not fussy and and he's a good sleeper."
And Eric, who entered the world on Valentine's Day, already met his half-brother Adam (Silverman's son from a previous relationship). "Adam came to London for his spring break from school. He adores his little brother and loves helping with him," the source said.
The source added, "It's a happy time. They're settling into their new life," and notes that Cowell and Silverman are not focused on an engagement and are just enjoying the present. Simon has a play that's officially opening on March 26, and the duo are expected back in New York City in April.
"I was born to be a dad," the 54-year-old music mogul revealed during his first post-baby interview with Extra. "I wouldn't rule out [more children]. Well, I got [dogs] Squiddly and Diddly, and I couldn't imagine Squiddly or just Diddly…I had a brother when I was younger, so I kind of think it's cool to have two or three…two."
Cowell admitted that he got emotional soon after his son was born and was surprised by the love he felt right away for his precious baby boy.
"I actually said to Lauren beforehand, 'What if I like the dogs more than him?' and she said, 'You're gonna be absolutely fine,' and then literally within seconds of him being born, I got it."