I see two real issues here:
1. Why do you say that your database is too big? If your queries don't perform well, maybe the fault is in the table design or the queries and not the number of rows. A database has to be designed with scalability in mind. After all, most databases grow.
If this is a drive space issue, I hope you have your data on a SAN volume so your network operations team can allocate more space for you. Again, most databases grow.
2. You want to archive by date but you don't know the date when the rows were created. If you don't have another column that will tell you what you can archive, then there's no real way you can archive. I would suggest putting an EntryDate column on all tables. While this will help you moving forward and do nothing to address your immediate problem, at least you won't have this problem come up again elsewhere.
If you have a column you can key in on to determine what you can archive, then all you have to do is insert the rows to archive into an archive table and then delete what you just archived. I would tend to look at #1 first though.