Keeping an inventory of vaccines is one thing the province is really good at. Right now the province has about 80,000 vaccines in inventory, so if they are running out at a supersite then there would have to be severe mismanagement and bad planning.
I think you're good.

They do about 7,000 doses a day or 50,000 a week, province-wide. More vaccine shipments are expected. The Supersites have almost 35,000 doses in inventory as of today.
Next week we will have over 70,000 doses delivered, then then we have 100,000 coming in the week after that. After that at least 87,000 Moderna doses come in per week.
Supply should not be an issue going forward.
https://www.gov.mb.ca/covid19/vaccine/reports.html