The problem is, by default one-off estimated tax (ES) payments can generate penalties for earlier quarter even if you paid all the tax so I don't think simply paying in Q2 avoids penalty unless you file Form 2210 Annualized Income method (see below).
By default, the underpayment penalty will be calculated as tho income is earned evenly thru the year, and estimated tax usually needs to be paid evenly to match it (what IRS refers to as "timely"); so 25% of this Q2 tax should have been paid in Q1 and will incur an underpayment penalty for a quarter on Form 2210. The good news is the penalty interest will only be for a few months until the Q2 payment resolves the underpayment.
Generally, keep in mind also you don't need to pay 100% of the 2025 tax, just the smaller of either - 100% of your 2024 tax (110% if AGI > 150k), or 90% of your 2025 tax; this is the 'safe harbor' amount you need to pay 'timely' during the year, either thru withholding or estimated tax, with the remaining balance due when you file.
I think you have 3 options, depending your situation and what amounts of tax/penalty are involved:
1. Accept some penalty for Q1 underpayment
2. Adopt the "Annualized Income" method to show the Q2 ES matches Q2 income and eliminate the penalty
3. Increase withholding to make your minimum "safe harbor" rather than use one-off ES.
Option #1 example, if you owed $4000 in tax and paid it all in Q2 ES, $1000 is by default due each quarter; you will have $1000 underpayment in Q1, $2000 overpayment in Q2, $1000 overpayment in Q3. The penalty on the $1000 underpayment will be 8% for 3 months (approx) = 2% * 1000 = $20. In this case paying full $4000 in Q2 isn't necessary either, there is nothing you an do about the Q1 penalty, but you would only need to pay $2000 in Q2, $1000 in Q3 and $1000 in Q4.
Option #2 - since you didn't know in Q1 to pay this yet... in order to not have a penalty for Q2 income paid with one-off ES in Q2 (same for unexpected income event like a Roth conversion or cap gain late in the year), you would need to adopt the "Annualized Income" method on Form 2210 when filing for 2025, and need to provide AGI/withholding per quarter (3/31, 5/31, 8/31, 12/31). Beware this method may fix the ES penalty but could conversely penalize you if you have to increase withholding later in the year for whatever reason, as withholding is otherwise by default considered to be 'timely' (it's just a total for the year, not by quarter like ES).
Option #3 - increase withholding on the W2 income for the rest of the year to make up the additional tax due (to make the safe harbor amount - 90% of your 2025 tax due), as long as you then don't use the AI method, because with the AI method you then have to specify the timing of your withholding vs. income and you are back to having an underpayment situation. Depends what amounts are involved, and keep in mind effects of self employment tax etc. The risk is if the W2 income isn't steady for the rest of the year and you can't withhold enough, then you're back to an underpayment situation on ES, possibly later than Q2.
More info on ES https://www.irs.gov/faqs/estimated-tax
More info on Form 2210 https://www.irs.gov/pub/irs-pdf/i2210.pdf
Not a CPA/Expert so just my 2 cents based on what you described. Hope this helps.
