The thing with migrating and loss of ranking will be down urls and the loss of links. Once everything is on your new site you will notice some url slugs will not be the same as your previous website. For example you may have had www.website.com/categories/tattoos whereas now you will have www.website.com/collections/tattoos. This goes for links that are being indexed by Google for whatever terms you're currently coming up for.
This makes migrating a little more work as you will need to work out what paths you have and then go through with the new urls. redirecting old to new so nobody hits a 404 page not found error.
Any backlinks you have will be to an old link on your previous so again need to redirect these to make sure the link juice is carried forward. For example if someone has mentioned your company on a high authority domain linking to your website you will need to make sure they do not go through to a 404 page not found once clicking from the baclink site.
As far as i'm aware this can all be sorted using the URL Redirects within the navigation section of your store. https://docs.shopify.com/manual/your-website/navigation/url-redirect
When doing this on a self hosted solution you would simply add them into the .htaccess file but unfortunately with Shopify it is not that simple.
Once the urls are all redirected to the correct places you should be okay. As long as the rest of the content is the same etc. You may see a slight decline over a week or so while Google crawls your new website but this is normal when going from one site to another. There will be others out there that say they didn't see any difference.
EDIT: Another thing to note. Over time you now know your quiestest time of the year. It's probably best to do the migration at this point even it if means holding fire for a few months. It gives you time to work out your url structure etc.
You can try with https://apps.shopify.com/litextension-amazon-to-shopify-migration-tool if you want to import products from amazon to shopify with keeping SEO URLs.
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