It is possible to method to generate SQLite3 database by writing PHP without any SQL?

Somewhat like django's models.

If you won't want to write SQL, possible is by using an abstraction layer, such as the Doctrine ORM.

It'll let it manipulate objects, around the PHP side -- and can cope with the database-related stuff (including compatibility between various kinds SQL databases).

No, to produce a database, you are gonna need to use SQL sooner or later unless of course you are utilizing a Database Manager. If you are using PHP, you should use the built-in libraries for being able to access databases, found here:

You may create database using PHP built-in libraries. Provided your hosting server enables.....