Have you sourced straw bales yet? Typically you can pick them up for $1-2 for a small 2 string bale. This year prices are nuts. You might be paying closer to $7+. Quality dirt will be much cheaper. I can get a large pickup load for $50.
Where are you? Do you have an abundance of leaves, yard waste, livestock manures, cardboard...? These items can be piled up and used as an informal raised bed. What's the quality of your native soil? How far along is the compost pile (direct sow into the pile)? The straw will decompose into nice light soil making a great amendment for natural soil but you do need to replace them every year or two.
But to answer your question, I would just make a chicken manure tea (mildly aged poop) and apply it to the bale when you cure it about a month before you sow. This will wash the nitrogen deep into the bale and not leave it sitting on the top. Cover it with black plastic if you want to warm up the straw and speed things up if you have a late spring.