Lasagna method on a budget with no time

Hello! I’ve just moved and I’ve also JUST had a baby, so I have little time and few resources to get my garden started in the way I’d really like. I also live in the Canadian prairies so gardening time here is precious because you get so little of it. That said, we are starting a garden from scratch at the new house. I’ve bought raised beds and a poly tunnel. I spent a LOT of money on making beds at the last house and the results weren’t amazing (the soil I bought ended up being garbage). This time, I’m hoping to do lasagna method beds and plant right into them and just hope for the best. My idea was cardboard or wood chip mulch/hay at the bottom, then layer hay and aged manure, leaving a thick mulch layer at the top. Is this a terrible idea? Is there a cost-effective solution or amendment you’d make to avoid issues. I’m mostly worried about the stability of this substrate mixture and also disease that could come from only using hay and manure. Thanks in advance.