How to Track "new customers" separately with new GTAG tracking

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for a few clients we're keen on updating their existing Google Ads tracking with an extra parameter to separate "new customers"  from existing ones. I understand we need to update the checkout GTAG with one line of code, but obviously, we need to have a variable that triggers the right boolean value.

1) is this possible ?

2) if yes, how would you upgrade the existing GTAG implementation:

<!-- Global Site Tag (gtag.js) - Google AdWords: xxxxxx -->
<script async src=""></script>
  window.dataLayer = window.dataLayer || [];
  function gtag(){dataLayer.push(arguments);}
  gtag('js', new Date());
  gtag('config', 'AW-xxxxx', {'send_page_view': false});

{% if first_time_accessed %}
 gtag('event', 'conversion', {
     'send_to': 'AW-xxxx/xxxx',
     'value': {{ checkout.subtotal_price | money_without_currency }},
     'currency': '{{ shop.currency }}',
     'transaction_id': '{{ order_number  }}'
{% endif %}

Thanks a lot for your input!