Find Oldest Date in Column but only if their is no date to the right

I have a formula that looks at a column and finds oldest date (=MIN(A7:A50) which works fine, but I do not want to count the date in column A if their is a date that shows up in a column that is to the right of column A. Currently their are many columns to the right of the column A with dates with numbers, dates, the word "DATE", or the cell could be blank.

Is their a formula that looks at column A and returns the oldest date but only on dates that do not have a date anywhere to the right?

Any help would be appreciated

The attached spread sheet has an orange cell BI6 that I'm try to put in a formula that looks at the column in green (AW7 thru AW34) and enters the oldest date into cell BI6, but if their is any dates to the right of the column in green (See cells in red with dates) then those cells in the green column with dates to the right in red would not be considered when picking the oldest date in the green column.

Resulting in formula in BI6 picking the oldest date between cells AW10, AW26, AW28, AW30, AW32, AW34.

Hope this makes sense.

Sorry, should have remembered. See attached.

I have asked myself that question! I did not create this spread sheet, the person who did no-longer works here. I was given the task on this existing file.
I appreciate your willingness to help but I have talked to my boss and convinced him to let me start over and create a new file. I'm going to cancel this thread.

Thanks again.

Thanks FDibbins! That works.