A lot of time and attention has been put into this topic. I've only included the first five articles/studies I came across in my searching. These should provide an adequate starting point for more searching on your part.
The most general statement that can be derived from just these articles and studies is:
While some small percentage of users will always use search first, most users prefer to use navigation over search, though (as stated by Katz & Byrne, 2003) this will very much depend on "the layout of the home page and the site’s information structure"
If you want to work out the right answer for your website and your users, you'll have to carry out some more research, and put together a hypothesis that can be proven or disproven by testing of your own.
From "Search Vs Browse on Websites" - MeasuringU.com
We noticed the more densely packed retail websites had higher search (>50%) but more data is needed to confirm that relationship. Given the sample of websites and tasks we can be 90% confident between 11% and 21% of users will start with search.
Across these independent data points collected over the last seven years, it seems safe to conclude that most users tend to start browsing over searching.
From "Search vs. navigate: How people behave on websites – do they search or do they navigate?" - Cludo.com
59% of web visitors frequently use the internal search engine to navigate on a website and 15% would rather use the search function than the hierarchical menu. What’s more, behavioral studies from the Nielsen Group and other research findings show that more than 50% of people visiting a start page on a website go straight to the internal search box in order to navigate.
From "5 Ways to Make Your E-Commerce Website Search Feature Convert" - Kissmetrics.com
responses generally showed over half prefer to use on-page navigation, while 47% of respondents prefer to filter down to specific product details (size, color, etc.) on the product page itself.
From "Effects of scent and breadth on use of site-specific search on e-commerce websites" - Katz & Byrne, 2003
“Given broad, high-scent menus, participants searched less than 10% of the time, but they searched almost 40% of the time when faced with narrow, low-scent menus; this is a practically-significant effect,” the paper states.
The paper goes on to identify that the rate search is used on a website is influenced by many things, but it’s especially affected by the layout of the home page and the site’s information structure.
From "Are there users who always search?" - Jared M. Spool, 2001
When we looked at the data from our study, we found that there wasn’t a single user out of 30 who always used the search engine first when looking for product information. None of the users in our study were search dominant. However, we did uncover some link-dominant users. About 20% of our participants chose links exclusively.
More relevant links: