The select a time calendar button appears on the product page, but not any other page out of the box. Unfortunately Shopify doesn't have a straightforward way to introduce the select a time button on the preview page only on the product page.
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To market the events from other pages like the home page, we suggest the Book Now button, see below:

You can promote your services directly on your homepage with the Book Now Button Widget. This maximizes your revenue by showcasing your events on any page of your store. An example of the Book Now Button Widget being active on a regular page of a Shopify website is below, with two options:

Let your customers see when you're available right away, driving them directly to the calendar pop up to book.

This is the default option which shows all of your events on a single pop up. The product description is used below the Select a Time button.

1. Click on the "Widgets" tab, and click on "Display on every page". You can customize colours here as well.

2. Select which view you want, like Calendar or List
3. Select the events you want previewed, up to 5
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4. Click the Book Now button on this screen to preview
5. Click Save and head to your website. Now, you should see this button on every page of your store to route your customers directly to your services.

See here for more: https://intercom.help/easy-appointment-booking/en/articles/7226912-feature-events-and-select-a-time-on-any-page-ie-home-page

You can use a single “Book Now” button that is embedded on your theme, like the example below. Here’s their site: https://fingerprintsbylivescan.com/.

This would be done outside the app since it would be editing the Shopify theme. See here for a Shopify tutorial: https://www.shopify.com/partners/blog/building-a-clickable-call-to-action-button-for-your-shopify-theme

You can also do this from the Navigation. Head to Online Store > Menus. Click the Menu and edit where it gets routed to.