Hi Adam,
The content of A1 may be irrelevant to to your table, but it is crucial to the application of conditional formatting to cell A1.
What you want is that A1 will be filled with green if B1 contains any data.
A1's fill colour can be changed by applying a Conditional format rule to that cell (A1).
Conditional format rules compare the contents of the cell to be formatted with either a fixed value or with the contents of another cell. In your case, you cannot use a fixed value, as you want the format applied to A1 to depend on the value entered in a second cell.
As you had not provided any information concerninb the content of A1, I provided a solution that did not depend on specific content (or lack of content) in A1. The solution does exactly what you want—it sets the colour both the background fill and of the text displayed in A1 to green when B1 contains any data.
With the new information (cell A1 may be empty), a simpler solution is possible. The simpler solution, though, requires cell A1 to remain empty—something that is difficult to guarantee if the document has more than one user, or if any user forgets that requirement.
The selected table is Main. Main-1 is a duplicate of that table, with the same CF rule applied to cell A1. Content has been added to B2 to trigger the rule. Cell A1 must remain empty to prevent the green fill being applied when B1 is empty. (To me, that makes the earlier solution the more stable, and thus more desirable) one.

Regards,
Barry