With so many websites asking for your email address these days, your inbox might start looking like the Wild West. However, if you don't access one of the accounts frequently enough, it'll sign you out. From there you'll just sign in, and you'll be able to access it when you click your profile icon in the future. Simply click your profile icon in the top right (mobile or desktop) and choose Add Another Account. If you have more than one active Gmail account, you can switch between them easily. Setting up filters in Gmail can help you parse through the noise of your inbox. This will filter your inbox so you can more efficiently use the select-all button to delete old emails.
If you're certain that you don't need any emails before a certain date, you can type in 'before:' into the search field and enter the date of your choice. Fortunately, there's another way to parse through the ancient digital weeds in your inbox. It doesn't take long for my inbox to spiral out of control, even if I'm liberally using the select-all-plus-delete combo.