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I signed up for salesforce and it never asked me to make an email. It made me go to a login page with a username and password. Since I dont have a password for it, I clicked "Forgot Password". The email to change my password was sent to my email but when I click on the link provided, it says my password change link has expired after 24 hours or this link has been used already. It is my first time using the link.
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It sounds like the email system you gave Salesforce has a security feature applied that checks the links embedded in all incoming email message to make sure they are non-malicioius before the message is placed in your inbox. Microsoft has a utility called Safe Links that does this, for example.
In this case, it would have already "followed" the link that Salesforce embedded in your email and that "used up" the one try that Salesforce allows on those links without setting the pw like you would have done if you were using the link first.
You need to apply for a Salesforce account with a different email address, one that does not have a system like Safe Links applied. For example, you could just get a new Gmail account, just for this purpose.
Just note that the usename you used before is now still on that original account so you'll need to use a different one for the new account. And also, the new account will have it's own custom-URL that appears in the email from Salesforce. Be sure to use that every time you log in to be sure your browser doesn't get confused between the two accounts when you try to log in.