How do I estimate my taxes if I want to file an extension without starting my return?

https://turbotax.intuit.com/tax-tools/calculators/taxcaster/

It depends. The simple method will be shown below which will eliminate underpayment penalty.

Generally, you can avoid the penalty if your total timely estimated payments and withholdings are greater than or equal to the lesser of:

• 90% of the total tax after credits for the current year, or
• 100% of the total tax after credits in the prior year
• See one exception below.

You can also avoid the penalty if the amount you owe is less than $1,000 as long as any estimated tax payments you made are timely.

Note: High-income taxpayers. If your adjusted gross income (line 11 of your 2023 Form 1040) is greater than $150,000 (or $75,000 if you're married and file a separate return from your spouse), you can avoid a penalty by paying at least 110% of your total tax from the prior year.