You need to gain 486 650 000 credits via exploration to go from aimless to Elite. With an average of 20 000 000 cr per hours (as calculated in TheYamiks video) it means you need a little more than 1 days of game to get it.

Remember that in order to get that amount, you need to have a dedicated ship to explore, with the good loadout, wich gonna take you additionnal time and credits.