In the past I've purchased Bitcoin by transferring funds from my checking account to Coinbase but that is taking 1 week. Can I buy Bitcoin using Cash? If so, how?
From what country you lived so that the community can give you a closed to specific answer.
There are your options:
a) At most of the cases, there are local crypto exchangers in a certain country which is way more easy and less hassle to used since it touches most of the local payment processor in your area.
b) Localbitcoins.com (as suggested above)
c) Bitcoin ATM (as suggested above)
d) Search for your local crypto group in social media and see if there are persons or group who have that kind of service. It's common now to save fees and minimize the risks of using third party exchanger. Of course as part of security measure, take a vouch for their legitimacy.
e) Continue to deal with Coinbase.
