Is it possible to declare double majors at separate time? For example, you declare English as your major during freshmen year then you declare psychology as your second major during Junior year making it double majors.
At most colleges it is possible to do that, yes.
However, in practice - if you want to graduate in four years you’ll need to have been taking the appropriate coursework all along. For example, psychology has a sequence of coursework that you need - usually you have to take 1-2 semesters of general psychology, then a semester of research methods and a semester of statistics, before you can take upper-level coursework. So it’ll be anywhere from 2 to 4 semesters before you can take upper-level coursework, and if you wait until your junior year to start it, you’ll be behind and won’t be able to finish the double major in four years.
However, let’s say you were an English major and started taking some psych coursework your sophomore year and then decided junior year you wanted to add it formally - then you could probably do that at most colleges.