What's the best possible relationship?
One to many.
Does the data structure of my two tables allow me to make a relation?
You will always be able to make a relationship. Whether it is a useful one depends on many things.
If not, what should I do?
Read and learn. You can start here. I have curated lots of information to get you started. https://exceleratorbi.com.au/knowledge-base/
Attached in capture my tables. I want to be able to highlight the expenses against the allocated budget.
Expenses table: Date, Invoice, Amount, Label, Supplier name, Heading, Site
Budget table: Heading in column and sites in horizontal.
Yep - there’s a lot to do. Read the articles I posted above.
Urgent
Really?