Is there a time frame to notify soldiers that they will be taking an APFT?

Nope.
The commander can do it whenever he/she wishes.
However for it to be a record APFT, they must be at least four months apart.

PFC (Join to see) NO, you simply must be told before the event if it is a "For Record" test
"(4) RECORD APFT IS DEFINED AS AN APFT ADMINISTERED BY THE COMMANDER AND SPECIFIED BEFOREHAND THAT THE RESULTS ARE FOR RECORD, THIS IS TO INCLUDE A MAKEUP OR RE-TEST APFT. A MAKE-UP OR RETEST APFT DOES NOT PREVENT A SOLDIER FROM TAKING THE NEXT RECORD APFT SCHEDULED BY THE COMMANDER. COMMANDER MAY ADMINISTER THE APFT AS OFTEN AS THEY WISH (FOR RECORD OR PRACTICE) AS LONG AS THEY ADHERE TO THE POLICY DESCRIBED BELOW:"

A. THE ACTIVE ARMY (AC), ACTIVE GUARD/RESERVE (AGR) SOLDIERS WILL TAKE THE APFT FOR RECORD AT LEAST TWICE EACH CALENDAR YEAR. SOLDIERS IN THE ARNG TPUS WILL TAKE THE APFT FOR RECORD AT LEAST ONCE EACH CALENDAR YEAR.

B. A MINIMUM OF FOUR MONTHS WILL SEPARATE RECORD TESTS FOR AC, AGR AND USAR TPU SOLDIERS. A MINIMUM OF EIGHT MONTHS WILL SEPARATE RECORD TESTS FOR ARNG TPU SOLDIERS. "

That said, If it was on the training calendar and you, the SM did not bother to read it, your lack of knowledge is your own fault.

If it is an unplanned off calendar event being thrown in last minute due to some missed requirement or drop dead task from higher, Id consider it piss poor planning on the Commanders part.

In general, other than a Unannounced UA, a commander wants to see his team successful, so it would be best not to "surprise" the team with an APFT for record.

I've done it ONCE, the company paid the price for ONE senior NCO who always managed to be absent the day of the record APFT...and his make up APFT done by "others" always had him near max and passing weigh in screen ...........
So the CDR, and company 1SG arranged quietly to have a company record APFT, it was announced at morning formation and happened immediate following. I wont say it was the best idea, and it was not "fair" but it was successful

Nope, its a command decision. Soldiers are required to maintain physical readiness at all times which means they can execute a passing APFT at any time.