It would probably be worth doing keyword research to find out what your target market are searching from on Google. The best free guide on this can be found here: https://backlinko.com/keyword-research
Once you have your keywords it would be worth populating your website’s meta data. It looks like you are using WIX, so this should help explain: https://support.wix.com/en/article/adding-seo-page-titles-and-descriptions-meta-tags
Are there any high profile people / influencers you know that have cats? It may be worth sending them one for their cat and hope that they like it (and then say so on social). Maybe have a look on Instagram etc.
Google Shopping are releasing a free version shortly called Google Surfaces, this will (sort of) allow you to have shopping ‘ads’ without having to pay for them. https://support.google.com/merchants/answer/9199328?hl=en
Hope this helps.