Yes, you can make estimated tax payments for the 3rd and 4th quarters, even though you did not pay for the first two quarters. If you end up paying more than necessary, you will get a refund of the excess when you file your tax return after the end of the year. There is no negative impact except, as you said, losing use of the money.
Usually people pay estimated tax only if they have significant income from which no tax is withheld. If your primary income is from a job where taxes are withheld and you get a W-2 at the end of the year, it might not be necessary to pay estimated tax. You can use the IRS Tax Withholding Estimator to figure out what you should each put on the W-4 form that you give to your employer to make sure that you have enough tax withheld.
