Posting an adorable photo on Instagram of himself laughing as he held his baby, Sandiford wrote: "Jimmy wishing his daddy a happy birthday," tagging Paige and his sister Sophie, who also appears on the Channel 4 show.
The post was in celebration of Pete's 27th birthday.
Pete first announced news of his wife's pregnancy in April during an episode of Gogglebox when he showed his sister a baby scan on his phone.
He was very excited to be a dad, saying: "Innit mad? I am actually going to be a dad to somebody."
The couple married in early September in an intimate ceremony after the arrival of their baby son, with Sandiford flashing his wedding ring during the National Television Awards in London.
As reported in OK! Magazine, he said at the time: "I'm married now! It was nerve-wracking but the best day of my life. Well, second-best day as I'm a dad now, too."
"I'm a proud father. He's a cool little lad. Takes after his mum. I slept on the train here, I'm so tired."
Sandiford added that he was "buzzing" to be at the NTAs as he was able to have a full night's sleep away from his baby. He also said that "[Jimmy] is basically a miniature version of me and Paige and that's what I always wanted so I feel well lucky."
Standing with him, Sophie said of Jimmy: "I'm a very proud auntie. I'm obsessed with him. I just keep saying, 'Can I hold him, can I feed him?'"
Jimmy has already made his TV debut alongside his dad and his aunt Sophie on Gogglebox, being cradled by his dad.
Pete was a doting dad as he snuggled with his son, with plenty of fans tweeting about the adorable scene.
Gogglebox airs on Friday nights at 9pm on Channel 4.
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