I'd start with a form so the user can fill these {type}/{province}/{town}/{search-term} and it will be the querystring. A form can use a get request. Or post and thereafter a get.
More than one way to achieve this.
Edit:
Also have a look at laravel scout. But for a "drill down" search really not needed.
but this would affect the SEO?
A query string doesn't affect SEO. SEO is mainly concerned with home page, meaning the main page a visitor is searching for in Google.
For example:
https://laracasts.com/discuss/channels/livewire/how-to-filter-posts-by-different-filters-to-the-url?page=1&replyId=939851
Has nothing to do with the main site:
https://laracasts.com/ // This need SEO, not a search once on the site.