His mother, Stacey Williams, said her son's interest in tank engines started as a toddler after older brother Sam decided to give all his Thomas the Tank Engine toys to his baby brother, who loved them.
"It's been a calming thing for him,'' Williams said.
"Right throughout his entire family, no matter what happened, he could always go back to the Thomas the Tank Engine stories, toys and videos and find calm.
"So it made so much sense that of all the times that he wanted to celebrate something - and he's never asked for anything in his life - this is what he wanted."
Williams decided to put out an appeal online asking for help to make her boy's dream come true.
A GiveALittle page raised just over $2500 and helped to get the whole family - including twin brothers Taitoa and Arapeta, 7, sister Te Aroha, 6, mum Stacey and her partner Richard Tidbury - to Auckland over the weekend.
The Glenbrook Vintage Railway happened to be holding a special Day Out With Thomas event that included rides on several steam trains decked out as the much-loved Thomas and friends trains, on the same day as Matthew's birthday.
Williams said it was an exciting thing to see her son's dream come true - and for them to all be with him also.
"There was a sense of that he didn't quite realise what was going on because it was overwhelming.
"But once we got on the train for the ride and everything else started to tick along, you could see his excitement.''
Williams thanked members of the public who had donated towards the trip and which ensured they could afford to make it happen.
"All I can say is that I don't know how to thank the entire community for what they did for us. Know that he absolutely loved it."