Make sure you have cold email notifications set up by email at a minimum. You need to respond to these as fast as possible.
If you use Slack, also set up the notifications for your Slack channel.
Make sure both of them are checked yes/turned on.

If you use Slack, click Add New, follow the instructions of how to add the Webhook to Slack, and then make a specific channel called #cold-email-replies

Turn On Cold Email Notifications - Month 2 · 10k Per Month Agency