I already found out that there is no way to bundle files in an .apk and have them on /sdcard, the best option so far being to download the large files upon first run. I came
Just an idea:
you can put your database.db into the assets folder.
if your database.db file is larger than 2Mb the system is unable to compress it, so you need other one options
you can rename your database.db for example database.jit or database.mp3 - which are not compressed, than at the first run you can rename it to database.db