Unfortunately you can't just copy the "hot" mdf & ldf files, even while no data is actually being written to the DB. As long as the files are attached to a SQL Server you cannot copy or move them. In fact I don't think Windows will let you even copy them as they should be locked by the server process.
The trivial solution is just using backup and restore, it's painless and secure. In fact there should be already be a regular backup process since you mention that this is production system, maybe you don't even need to actually take a backup, just wait for the next one to take place and use it to restore. On SQL Server the backup/restore process is really straightforward, probably one of the easiest on all the RDBMS ecosystem.
Any other method will be more difficult and likely yield worse results. I wouldn't recommend them at all. You could try to copy the files using VSS (Volume Shadow Copy) and see if you get consistent enough files to attach. Alternatively you could create an empty database and just export all the tables, views, procedures, etc.