I assume you are talking about the built-in browser prompt that asks if the user wants to allow/block push notifications, as opposed to a custom solution of your own.
First of all, these are extremely annoying for the user and very obtrusive. Having one of these pop-up without me taking any action is an immediate "block".
The second problem is that there are only 2 options: Allow and Block. "Block" is a negative word. It's like saying that the site is spam, and it is no surprise that browsers are starting to treat it as spam.
So putting this at the very start of the site interaction is a bad idea. How can a user be expected to click "allow" when they haven't even been on your site long enough to know what they are agreeing to? You will almost always get a "block" in those instances.
I recommend that if you want to support push notifications on your site then you should make this a user options somewhere. Sure, you can "advertise" this feature on your landing page if you want to promote it, but let the user read some information about what it does and what type of notifications you will be sending. Then if the user wants them let them click a button and then you can prompt for confirmation. This way, they will almost always click on "allow" because they have already made the decision to do so.
I also suggest you keep in mind that (in my opinion) this feature won't be around for much longer. It is too easy to abuse for spammers and attackers and I expect this tactic of blocking sites with a bad reputation is likely just the first step in it's demise.
In summary. Don't automatically show the prompt. Provide the user with some information about what the notifications will do. Give the user the option to agree to them before the prompt it shown.