First, Trump has decided to appeal the order signed on Friday, even though Merchan all but declared that Trump will face no prison time. But he's going beyond a direct appeal, which opens up the possibility of immediate appellate action:

Trump’s lawyers said they plan to ask a state appeals court to reverse Judge Juan M. Merchan’s decision last week, which set the case for sentencing on Friday — little over a week before he’s sworn in for his second term.

In a pair of rulings in recent weeks, Merchan rejected Trump’s bid to throw out the verdict and dismiss the indictment on presidential immunity grounds and because of his impending return to the White House.

In a decision last week, the judge signaled he is not likely to sentence Trump, a Republican, to any punishment for his historic conviction on 34 felony counts of falsifying business records. Acknowledging the demands of the transition process, he had given Trump the option to attend in person or appear virtually by video.

At the moment, Trump has to appeal this decision to ... Juan Merchan. That obviously won't go anywhere, but that order does allow Trump to start escalating the issue. The New York Times explains how Trump can sue Merchan in the state appellate court, and how fast that might produce results:

Although that request is most likely doomed — the judge, Juan M. Merchan, was the one who scheduled the sentencing — Mr. Trump’s lawyers disclosed in the filing that they planned to escalate their effort. If the judge does not pause the sentencing by 2 p.m. on Monday, the filing said, Mr. Trump will “seek an emergency appellate review.”

Hoping to persuade a New York appeals court to intervene, Mr. Trump’s lawyers plan to file a civil action against Justice Merchan and seek to freeze the sentencing, according to the filing. It is unclear when they will file that action with the appellate court, but it could come as soon as Monday. ...

Mr. Trump’s lawyers said they planned to both appeal Justice Merchan’s rulings and file an action against him as a so-called Article 78 petition, a special proceeding used to challenge decisions made by New York State agencies and judges. In essence, the president-elect would bring a civil case against the judge to unwind his recent decisions to uphold the conviction and schedule the sentencing.

The appellate court could act fast. An appellate judge could rule on the petitions as soon as Monday, deciding either to grant or deny an interim stay of the sentencing. While ordinarily that judge’s ruling would only be temporary — a full panel of appellate judges is supposed evaluate Mr. Trump’s claims in the coming weeks — the case against the president-elect is running out of time.

They could act fast. There isn't anything that forces them to act fast, of course. The pace at which they do address it could be a good measure of their assessment of the Bragg/Merchan lawfare that has unfolded over the last two years. I'm not as sanguine as some that New York's appellate courts will recognize the corrupt machinations of Bragg and Merchan, but then again, they have not yet had a chance to intervene. 

Merchan's decision to move ahead on sentencing and "certifying" the verdict opens up that option. So what is an "Article 78" proceeding? It allows for an expedited review of official actions by the executive branch and regulators in the interests of justice. This is different than a judicial appeal, which would only be allowed after sentencing. But does Article 78 apply to judicial actions? According to one appellate law office, it can -- under very limited circumstances:

An Article 78 Proceeding cannot be used to challenge criminal convictions or criminal sentences.

However, it can be used to challenge many other actions by Judges, such as where a Judge has acted beyond his authority (Writ of Prohibition) or has failed to act (Writ of Mandamus).

Presumably, Trump and his legal team will focus on Merchan's refusal to hold a hearing on his immunity claim after the Trump v US ruling by the Supreme Court. Having established that refusal in the denial of the motion and then the scheduling of a sentencing hearing, Merchan may have opened a window for the appellate court to act via an Article 78 proceeding. That only works, though, if the appellate court really wants to intervene in this case. It's just as easy, or perhaps even easier, to simply shrug off a challenge via Article 78 and let Trump pursue the normal appeal process after sentencing. 

Don't forget that this is not the first time Trump and his legal team have tried this strategy. They tried to use an Article 78 lawsuit against Merchan in early April to stop the trial and get a change of venue. The issue at hand was much less substantive than the immunity claim, though:

In a separate proceeding, he indicated that he planned to file an unusual type of lawsuit against the judge overseeing the case, Juan M. Merchan.

Two people with knowledge of the matter said that Mr. Trump’s lawyers on Monday had planned to file the action calling on the appeals court to overturn a gag order that Justice Merchan recently imposed on the former president. The order prevents Mr. Trump from attacking witnesses, prosecutors and the judge’s own family.

Court records showed on Monday that Mr. Trump had begun the process of filing the action against Justice Merchan, though the papers were not immediately made public.

An online court docket where Mr. Trump is expected to file the so-called Article 78 action — a special proceeding that comes in the form of a lawsuit and can be used to challenge New York State government agencies and judges — showed that the related paperwork was sealed.

This attempt was mainly predicated on the inability to appeal rulings within the New York judicial system until the verdict and sentence are formally entered. It also had significant political value for Trump in painting him as a victim of judicial censorship, and arguably paid off for him too. At the pretrial stage, the appellate court likely felt that no issue was ripe enough for an Article 78 proceeding, let alone substantive enough.

This is a more substantial issue, though it remains to be seen whether it's substantial enough for the appellate circuit to act. It has to do with the integrity of the indictment, prosecution, and verdict. While it doesn't directly challenge the latter (which is apparently not permissible in this process), there is a clear argument that Merchan acted in an unjust and capricious manner in not granting a hearing on the immunity claim. 

Since jurists usually take the paths of least resistance -- not to mention personal risk -- I'd assume that the court will shrug off this lawsuit. But the spectacle of political lawfare in both the Merchan and Arthur Engoron courts must have had some impact on the judiciary at the higher level. These jurists may be more motivated to put an end to politicized prosecutions than we think. We may find out soon, too.