Did Nazi Germany start out defunding the police?

NO!!

In 1933 Hitler appointed Herman Goring Minister of the Interior. His first orders were to defund and eliminate the police departments so that they would not interfere with his Brown Shirts

The above meme confuses a lot of aspects of the Nazi Machtergreifung into a factually incorrect narrative. Göring was the Prussian Minister of Interior and this gave him broad authority over the policing of Germany. And this was a fundamental component of destroying the Republic. But there was no defunding and elimination of the existing police force. Quite the opposite process occurred.

As Prussian Minister of the Interior, Göring had broad powers over the police for much, although not all, of Germany. Göring used his authority to purge any police officials who were Social Democrats or otherwise would stand in the way of the NSDAP's program to destroy the Republic and meet vengeance against the NSDAP's political enemies. SS-Gruppenfuhrer Kurt Daluege became Göring's personal representative to comb out potential disloyal members of the police and he later became the head of the Ordnungspolizei (regular uniformed police/ORPO). So the Prussian police forces did lose some members, they were neither defunded nor eliminated. Instead, they became tools of Nazi repression.

But the focus on purges and centralization of power obscures the fact that Göring did not have to do much to transform German police into an instrument of a dictatorship. Although there had been clashes between NSDAP street brawlers and the police, the Weimar-era police and justice departments were notorious for being "blind on the right eye," meaning they were less inclined to deal harshly with political crimes from the right. Hitler and other NSDAP leaders, for example, got what amounted to a slap on the wrist for committing high treason for the Beer Hall Putsch. The Republic was very quick to ban the KPD's paramilitary Roter Frontkämpferbund in 1929, but dragged its heels to ban the Sturmabteilung (SA) even though the SA was exceptionally violent, even by the standards of the day.

So the German police, with few notable exceptions, were politically primed to fall under NSDAP rule. Göring's various initiatives centralized German policing to an unparalleled degree, which suited a number of Republic-era critics who felt that German policing was too decentralized to meet modern crimes. By the same token, the NSDAP's emphasis upon law and order as the main rationale for these measures also opened up the police to apply state power to alleged deviants and asocials. The Machtergreifung not only witnessed a crackdown on political enemies but also attacks on those outsider groups. The Nazification of the police counter-intuitively coupled centralization of policing with elimination of rules regulating German police. On 17 February 1933, Göring instructed Prussian police to use firearms against enemies of the state. This marked the start of an era where police violence became more routine under the new order as legal safeguards muzzling them were removed.

The most significant initiative Göring introduced in these early months was to deputize the SA and the paramilitary of the NSDAP's allies on the right as police auxiliaries. This allowed the SA to place various political enemies under protective custody without formal charges. The orgy of SA violence caused some friction with the (largely intact) police forces and justice ministry. But the response of these groups was not resistance, but a routinization of political terror by the state. Judges in the Third Reich, for example, followed the tenor of the dictatorship and applied increasingly harsh penalties on criminals. The Third Reich's judiciary, the bulk of whom began their careers in the Kaiserreich and Republic, hewed to the state's notion that criminality was a violation of the Volksgemeinschaft.

The control of German policing soon became a political prize among the NSDAP with Himmler winning after some internal tussles. The German police expanded greatly both in numbers and in their missions. Police departments did not disappear in the Machtergreifung. Instead, they were not only larger, but emerged as a more unrestrained force in dealing with the German public they were supposed to protect.