That said (above about your chosen plants being cool weather growing plants) you could do a round of lettuce, radishes, etc. and THEN plant another round of beans or tomatoes or whatever. Beans like hot weather. Here in Ohio you should not rush to get your beans in - early June is fine.
If the community garden is really promoting square foot gardening - and only giving you a very small spot to plant (4 squares) they should be promoting that you make the most of those 4 squares by planting tight and planting more than one round of crop if possible. Of course if you do flowers you don’t need to replant - but still plant for good coverage in the square - more plant = less weeds!