How do I detect if sqlite3 created a database file?

I'm writing a program that uses a sqlite3 database file to store its data. If I open a database file with

sqlite3_open_v2(filename, &db, SQLITE_OPEN_READWRITE | SQLITE_OPEN_CREATE, NULL)

the database file is created if it does not exist. How can I find out if the database file existed prior to opening it? The sqlite3 shell uses code like this:

  /* Go ahead and open the database file if it already exists.  If the
  ** file does not exist, delay opening it.  This prevents empty database
  ** files from being created if a user mistypes the database name argument
  ** to the sqlite command-line tool.
  */
  if( access(data.zDbFilename, 0)==0 ){
    open_db(&data, 0);
  }

This code however has a race condition when the database file is created by another process after the access call and before the open_db call (time-of-check vs. time-of-use).

Another answer (that I can't find right now) suggests to check the application_id and user_version fields. If they are zero, a database was just created. I researched this approach and found that numerous applications actually don't bother to set these fields in newly created databases, so this approach is fuzzy at best and I don't think it solves my problem.

Is there a method to find out if the database existed prior to opening it that does not involve a race condition like this? It is also acceptable if I can merely find out if the database file was initialized (as in, a truncated file was populated with a sqlite3 header) by sqlite3.

The purpose of having such a routine is to be able to find out if I need to create all the tables I need in the database. I don't want to accidentally overwrite another file placed there by a different application.