I can talk about France and Georgia (the latter not being this interesting considering our International Elite train abroad)
In France you go through different "Levels", it is not necessary to do them all, you can start at a National Level or go straight from the lowest to the highest level, usually girls who compete national level at a young age can be selected to enter a national training center (there are about 6 of them i think, they can make it to training center at every age >9 ) then they are in the elite world, then can for different reasons go back to club gymnastics. To compete at Elite nationals they need to score a certain score.
In 2018 those scores were:
48.5 Seniors
46.5 2003 juniors
44.5 2004 juniors
41.5 2005 Hopes
40.5 2006 Hopes
42 2007 Nationals
41 2008 Nationals
In Georgia we are scored on FIG code really early (SV modified for lower levels) we have no choice for elite gymnasts so usually they are selected by our federation president and head coach Rusudan Sikharulidze (former elite gymnast) to be sent to international meets (based on videos if they train abroad)