How to deploy embedded database contained within .jar file?

Question

I'm currently developing a java application where users shall be able to create profiles, sign in with their login data, store some information connected to their user profile, etc. within a database. As the application should come lightweight and the normal user who isn't as technophile as developers might not want to manually set up a database on his system prior to being able to use the application or even might not be able to do so.

Hence what I am going for obviously will be an embedded database. As I've already read through several posts dealing with embedded databases and how to access them I'm already aware that I won't be able to simply pack an initialized - yet empty - database within my .jar file and let users store new data in it as it will be static and read-only when packed within the .jar file.

But as obviously there has to be some way to set a database up without even bothering the user with its creation or configuration I'm now asking myself What are the usual ways to do so? How is this typically done? Because obviously there are a lot of applications that use non-static embedded databases.

An idea I've come up with is creating such an empty, initialized database which then will be packed within the .jar file and upon each launch of the application, the application looks for a appropriate database file within its current location and if it doesn't find one it simply copies the empty database packed in its .jar file to the folder. But I'm not sure if this would actually be enough to make this work or if this is actually properly achievable or if there's no better way to do so.

I'm really curious for what a typical solution of this scenario looks like and thanks in advance for your input and ideas on this.