Please do. Yes it is true that some firms do give places earlier, but for one, I’ve noticed this recruitment cycle is slightly slower understandably with COVID-19, not a lot of ACs have even been given out and a lot of ‘rolling’ firms still say they won’t tell you until after the deadline. Also, the majority of people will apply within one week of the deadline. Just to put that into perspective!
Every time I’ve got further in an application, it’s always been a rolling app that I submitted ‘late’ on. People told me I didn’t have a chance and if I listened to them I wouldn’t have got to that. If you want to apply to the firm and it’s within the deadline, do it