Cumulative SumIF or Index match across multiple columns

Hi all, first time poster, long time googler here.

My issue is I am looking for a cumulative sumif or index match type solution to solve my problem (example attached). I have data over 2 sheets, first sheet is where I want the cumulative totals to be listed by month (in columns) and the second sheet is where the data is stored and it can be in any order in the rows on the sheet and will be added to over time, that's why I don't want to use a fixed =SUM formula as the order of the rows could change.

If I need to add more info to help solve this pls let me know