For example, when JAXA launches a rocket, or people count the seconds to the New Year, do they use し or よん to count 4? do they use しち or なな to count 7?
Usually when you count, you use
よん for '4' and
なな for '7'. That applies to when you count down.
じゅう きゅう はち なな ろく ご よん さん に いち
However, in some situations, pronouncing a certain sequence of numbers became so frequent end became a fixed expression. In that case, '4' and '7' may be pronounced
しち, respectively. That includes a situation of counting up:
いち に さん し ご ろく しち はち きゅう じゅう