Those 300K were evacuated over the course of 9 days so all 300K weren't standing and waiting on the beach for boats to show up the whole time. There were likely thousands on the beach at once, but you can see in the table 68K were the most evacuated in one day.
Troops landed from Dunkirk
27 May – 4 June
Date Beaches Harbour Total
27 May – 7,669 7,669
28 May 5,390 11,874 17,804
29 May 13,752 33,558 47,310
30 May 29,512 24,311 53,823
31 May 22,942 45,072 68,014
1 June 17,348 47,081 64,429
2 June 6,695 19,561 26,256
3 June 1,870 24,876 26,746
4 June 622 25,553 26,175
Totals 98,671 239,555 338,226
https://en.wikipedia.org/wiki/Dunkirk_evacuation