Little Wolfe was born more than seven weeks early to Stephen Crawshaw, from Illingworth, and his wife Louise while they were away in Turkey.
He has been receiving treatment in intensive care in Turkey but has now come off a ventilator and has been able to have his first cuddle with Louise.
Loved ones said: "He is still getting fed through a tube as he is a little young and doesn’t have the suckle reflex just yet. They are hoping it will come soon though.
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"Louise had her first cuddle with him today for a whole five mins and it was amazing. He is so tiny."
As reported by the Courier, Stephen and his wife Louise are facing steep medical and accommodation bills in Turkey, and it would cost around £50,000 to charter an air ambulance to fly Wolfe back to the UK.
The couple were married last month at Hazlewood Castle, near Leeds, and were away with their nearly-one-year-old son Ronnie and Louise's three other children for their honeymoon when Wolfe was born.
The couple had insurance, as well as a fit to fly note from Louise's midwife, but their insurance company has told them Wolfe would have needed to be born eight weeks early for them to pay out - and he was born seven weeks and five days before his due date.
Stephen, 28, has been serving with the Yorkshire Regiment since he was 16, and has many family members in Halifax.
The couple's loved ones have set up an online fundraiser in a bid to help the couple during their ordeal.
To donate, visit https://www.gofundme.com/f/this-family-get-this-beautiful-boy-home