If you're trying to track down a specific message, you can narrow down your search criteria in both Outlook and Gmail to pull up the most relevant results.
In the free web version of Outlook, click the "Filters" option in the search bar to refine results by the sender, recipient, subject line, date, and more.
You can click the down arrow in the Gmail search bar to access similar options. Gmail also offers more granular filters, such as the option to only find emails that have a specific word or phrase.
It's also possible to search for emails in Gmail by by typing a qualifier in the search bar followed by a colon and the search query.
For example, if you want to see emails sent to Emily, type "to:" in the search bar followed by Emily's email address. If you've corresponded with Emily before, her email address should come up as an autocomplete option once you start typing her email address.