At first you can store the first date as a UNIX timestamp. Then you can compare the current timestamp in seconds with the old, first saved timestamp whenever you want to check if 7 days past or not like below.
Calendar cal = Calendar.getInstance(Locale.getDefault());
long firstTimestampInSec = cal.getTimeInMillis() / 1000;
Then you can compare by looking if 604800 seconds past or not.
Calendar cal = Calendar.getInstance(Locale.getDefault());
long currentTimestampInSec = cal.getTimeInMillis() / 1000;
int oneWeekAsSec = 604800;
long firstTimestampInSec = getOldStoredTimestamp(); //First stored timestamp as seconds
if(currentTimestampInSec >= firstTimestampInSec + oneWeekAsSec){
System.out.println("It's been a week");
}
else{
System.out.println("It hasn't been a week");
}