Use PostgreSQL to generate Unique ID for row upon insert

So I currently have a primary postgres database that handles multiple users from different apps. So one of the issue regarding concurrency is that when say AppOne and AppTwo want to add users at the same time.

Currently what is happening is AppOne will generate a random number (must be 10 digits long) and then check if the value exists in the database, if it doesn't exist then it will insert the user with that value in a column called user_url (used for their url).

Now as you can image, if in between the time for the generation, check, or insertion AppTwo makes a request to add a users we can have repeated unique values (it's happened). I want to solve that issue potentially using postgres triggers.

I know that I can use transactions, but I don't want to hold up the database, I'd rather it created the unique number sequence through a function and trigger on the database side, so as I scale I don't have to worry about race conditions. Once the trigger does it's thing, I can then get the newly added user with all of it's data, including the unique id.

So Ideally

CREATE OR REPLACE FUNCTION set_unique_number(...) RETURNS trigger AS $$
 DECLARE
  BEGIN
   ....something here
  RETURN new;
END;
$$ LANGUAGE plpgsql;

CREATE TRIGGER insert_unique_url_id BEFORE INSERT ... PROCEDURE     
set_unique_number(...);

it would be a function that generates the number and inserts it into the row, which would be run by a trigger of BEFORE INSERT. I may be wrong.

Any help/suggestions would be helpful

Thanks