How to create slack alerts for new sign-ups on our SaaS?

This is exactly the problem Trial Hook solves out of the box. You get the Slack alert, but also job title, company, LinkedIn and location enriched automatically - no Zapier, no webhooks to configure. And it's FREE! Check it out: https://www.trialhook.com/

I am using Segment and they have Slack as a destination, so you can do it that way.

So my guess is that you want to action on your analytics?

You're describing a light use-case, you can do this Engageful.io with our Slack iintegration.

I use it myself.

Wanna check it out?

if you ask every new customer to fill in an onboarding google form, i build slacknotify.app which you will find helpful to do just that

I second Zapier.
It supports 100 alerts/month in a free version. Not sure why to spend time on setting up something else, if this option exists (for start, ofc)

I run a slack channel nad use Zappier to do a lot of integrations. Maybe you will find something there