Yes, although that would be a little unusual. It’s often smart to get the administrator of the estate appointed before filing a wrongful death case because the administrator of the estate will usually bring additional claims that will be a part of the same lawsuit. (For more detail about this, see the question “What compensation is available in Georgia for a wrongful death case?” above.) However, it is not strictly necessary.
There could be case-specific reasons to file the wrongful death case before the estate administrator has been appointed, even though that is an unusual step. For instance, you might need to get the case filed before some deadline, such as the statute of limitation or an ante litem notice requirement. Or if death was instant, such that there was no pain and suffering and no medical bills, you and your lawyer might decide not to bring claims on behalf of the estate, but only to bring wrongful death claims.
In special circumstances—such as where “the surviving spouse is absent, disabled, has declined to pursue the claim, or has no relation by blood or law to the surviving children”—courts have allowed the children of the decedent to bring a claim even when the decedent had a surviving spouse. Mann v. Taser International, Inc., 588 F.3d 1291, 1311 (11th Cir. 2009). A surviving spouse may lose his right to bring a wrongful death claim if he abandons his children and cannot be found. Brown v. Liberty Oil & Refining Corp., 261 Ga. 214, 215-16 (1991).