I filed my taxes on May 2, 2020, I was given a estimated date of May 23, 2020 and yet it still hasn't been deposited

The IRS can look at your 2018 or 2019 return to issue a stimulus check.  If they do not have a 2018 return then you may be waiting for them to finish processing 2019 before they will be able to use it to issue your stimulus check.

TurboTax has no control over your stimulus check, nor can TT track it for you or tell you when the IRS will issue it. Refer to the sites linked below:

https://www.irs.gov/coronavirus/economic-impact-payment-information-center#nonfilertool

https://www.irs.gov/coronavirus/get-my-payment-frequently-asked-questions

https://ttlc.intuit.com/community/tax-topics/help/how-will-the-stimulus-package-impact-me/00/1393859

IRS phone lines supported by customer service representatives for both taxpayers and tax professionals are not staffed at this time. To check on regular tax refund status via automated phone, call 800-829-1954. (This line has no information on Economic Impact Payments.)

https://turbotax.intuit.com/tax-tools/efile-status-lookup/

TurboTax gives you an estimated date for receiving your refund based on a 21 day average from your date of acceptance, but it can take longer.  Many refunds are taking longer during the pandemic. 

Once your federal return has been accepted by the IRS, only the IRS has any control. TurboTax does not receive any updates from the IRS. Your ONLY source of information about your refund now is the IRS.

You need your filing status, your Social Security number and the exact amount  (line 20 of your Form 1040) of your federal refund to track your Federal refund:   

https://www.irs.gov/refunds

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

https://ttlc.intuit.com/questions/1901548-why-do-some-refunds-take-longer-than-others

If you chose to have your TurboTax fees deducted from your federal refund, that will take some extra time, while the third party bank handles the refund processing.

https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions

https://ttlc.intuit.com/questions/2840013-does-accepted-mean-my-refund-is-approved

https://ttlc.intuit.com/questions/2724106-my-return-is-accepted-but-still-not-approved-is-there-a-problem-should-i-be-worried