The plant has plenty of blooms. They dry up and fall off in a few days.
Certified GKH Gardening Expert
This is caused by a pollination issue. Mostly, tomatoes are wind pollinated, but in damp/rainy weather or very hot weather the pollen gets sticky and does not travel well. You may need to give it some help. These articles can help: https://www.gardeningknowhow.com/edible/vegetables/tomato/pollinate-tomatoes.htm
This article should help: https://www.gardeningknowhow.com/edible/vegetables/tomato/tomato-blossoms-no-tomatoes.htm