1)Safe drop system in Payday 2 differ from loot drop system of CS:GO.
2)Safe drop system in Payday 2 have no global drop timer.
3)Safe drop system in Payday 2 have local timers for each player.

1)Record on Steam overlay random amount of time in range between 2 and 9 hours. I think this time determined by random number generator every each time for each player.
2)After recording this amount of time, need to play fast contract to obtain card drop screen.
3)No need to play the game whole amount of time. Need just to record it on overlay.

After safe drop, will be applied timer of cooldown to next safe drop in range between 5 and 7 days. I think this timer of cooldown determined by random number generator every each time for each player.

1)Record on Steam overlay random amount of time from last safe drop.
2)Wait cooldown of safe drop.
3)Play fast contract and obtain card drop.

If you have 2nd steam account without Payday 2, it is possible to connect it through "Family Sharing" and gain safe drop by above-described remarks.