Count only new occurrences within specific dates

I can't seem to find a good solution to my problem. I have a registry list of names with dates of attendance. What I need it to identify only New occurrences that occur within 2 dates. So anybody who attended between 7/1/23 and 8/31/23 AND have never attended before should be counted.

I have added a "Met" column which only identifies who attended within criteria dates but like it to also show new people.

In the example ("New?" column):

1. Danny Hoover and Susan didn't get counted since they never attended within criteria dates.
2. Brant White didn't get counted because even thought he attended within criteria dates, he also attended before on 4/1/23......so he is not new.
3. Callie would be counted for only 7/12/23 since date is between criteria dates.

I'm thinking its a combination of Countif formulas......?

Thanks Hans for your response. How would this work if I had to use the formula in column H to drag down? I just need each row to be identified as "New" if it is in fact new.