Has anyone ever escaped Darkseid's omega sanction of their own power, and if so, how?

The battle of the New Gods which led to Final Crisis occured due to Darkseid having acquired the Anti-Life Equation. In this battle, Darkseid manages to destroy the entirety of the Fourth World due to which the New Gods are incarnated as humans on New Earth since they don't have their Fourth World to exist in as their typical selves. During the climax of said battle, Orion "kills" Darkseid; but Darkseid, being Darkseid, does not die immediately even though he's in the process of dying throughout the story arc. This "fall" of Darkseid makes Darkseid's true form fall through the multiverse. Darkseid's true form is a higher dimensional one and thus, cannot be accommodated within the lower dimensions that the DC multiverse exists in. The combination of him physically falling through the multiverse and him being in the process of dying is what begins the end of the multiverse. This is what the ultimate crisis in Final Crisis is. Darkseid inching to his death accelerating the rate at which the multiverse was nearing its end demonstrated that his being in the process of dying was also tied to the multiverse ending, not just his physically falling through the multiverse. After falling through the multiverse, Darkseid also incarnates as a human named Boss Dark Side. A contract is arranged between Boss Dark Side and the Sheeda where the Sheeda have agreed to assist with finding the New God incarnates and killing them, harrowing the entire planet in the process if that is what it takes, in exchange for Aurakles who is the first superhero on New Earth.

Shilo Norman, the third Mister Miracle, who has been an ally to the New Gods is the only "avatar of freedom" left and is sought by Metron to be the "New Gods' weapon" against Boss Dark Side. His avatar of freedom status is more directly exemplified when, later in the story arc, he frees Aurakles to render Boss Dark Side's contract with the Sheeda moot, escapes his own grave after "having died" (his Motherbox had absorbed his consciousness), manages to resist the Anti Life Equation, and when the Victory of Evil is finally brought forth, as declared on panel, due to the death of the Avatar of Freedom when he finally died. Boss Dark Side is already aware of his avatar status and him being sought after, so he places Shilo Norman in Omega Sanction remotely in Seven Soldiers: Mister Miracle #1. Even though everything seems weird throughout issues #1-#3, it's not explicitly stated and is neither apparent to the reader that Shilo has been placed in Omega Sanction. It only becomes apparent in issue #4; where weird keeps getting progressively weirder. Eventually, this is what happens in issue #4:

Shilo Norman manages to escape from the Omega Sanction, although it can be argued that he had some assistance from Metron. It can be ascertained that Shilo was placed in Omega Sanction in the first issue itself, as upon escaping, Shilo finds himself inside the same black hole that he was going to attempt escaping as a stunt in the beginning of the first issue.

It's not known if the personification of Omega Sanction appears to everyone who is placed under it and if the provision of at least attempting to talk Omega Sanction out of keeping the victim under itself is standard. It is possible that it only happened due to Darkseid having been incarnated as a human and thus being severely depowered. Shilo succeeding at talking Omega Sanction out of it could also be a result of the same. Then again, Shilo being an archetype of escape artistry and an avatar of freedom is likely a factor too. Other New Gods also appeared in the iterations of Shilo's life within Omega Sanction, not just Metron, albeit in their human incarnations. Metron is the only one who somehow managed to appear to Shilo in his typical appearance, although those appearances were always outside the Omega Sanction. Though Shilo was unable to recognize the human incarnations of anyone except Metron, which is obviously a consequence of the Omega Sanction itself, what's not known is if it's routine for the New Gods to appear and interfere within the Omega Sanction. It could be another one time thing due to Darkseid being somewhat depowered. However, it's not possible to confirm these hypotheses since the only other instance of Darkseid using the Omega Sanction was on Batman, which wasn't a typical case of being placed in Omega Sanction.