Ms Williams said she didn't know if meeting Thomas the Tank Engine was even possible.
"I vented on a group Facebook page and someone turned around and said there is a life-sized Thomas the Tank Engine that Glenbrook station brings out twice a year in New Zealand. So I started researching."
She said when she contacted the company it just so happened one of the two dates was November 11, which is Matthew's birthday.
"They have been absolutely amazing. They are going to give Matthew a free entry but we need to raise funds for transport and accommodation for the whole family," Williams said.
The givealittle page was started on May 26 and has already raised $470.
Williams, who owns Stacey's Cakes, said she will also be fundraising through her cake business.
"Matthew is amazing, everything he has achieved in his life is more than we ever anticipated," she said.
He is completing his first unit in food handling and safety with Takiri Mai Ata Whanau Ora Collective. After completing the certificate he plans to work for his mum helping bake cakes.
To make a donation visit Matthew's Givealittle page.