HOW did you set the default language of your Website?

Did you follow the documentation?

https://www.odoo.com/documentation/17.0/applications/websites/website/configuration/translate.html

WHAT was the result?  It is hard to answer your question because we don't know what you tried and what you mean by "not the same as I wanted".

Something you should know about how Odoo sets the language on the Website:

1) First, Odoo checks the GeoIP of the user. Basically, what location in the world is the User accessing the database from. If the country code for that location has a default language that matches one from the Website, Odoo will use that first.

2) Second, Odoo checks the browser language set for the User's browser. Similarly to the approach above, if that language code matches one from the Website, Odoo will use that.

3) Last, Odoo will check the default language set on the Website and use that.

As you can see the default language on the website is only used if Odoo can't determine the language using the first two approaches.

in your  custom module, you can try something like below 

from odoo import models, http

from odoo.http import request

class Website(models.Model):

    _inherit = 'website'

    def get_response(self, path, query_string, anchor, response=None):

        # Check if the user is visiting for the first time (no cookies set)

        if not request.httprequest.cookies.get('visited_before'):

            # Force Arabic language

            lang_code = 'ar'

            request.env['ir.http']._set_cookie_language(lang_code)

            # Redirect to Arabic version of the page

            url = request.httprequest.url.replace('/en/', f'/{lang_code}/')

            return request.redirect(url)

        # Set a cookie to indicate that the user has visited

        response = super(Website, self).get_response(path, query_string, anchor, response)

        response.set_cookie('visited_before', '1')

        return response