Medical science does not know yet how paracetamol works

Following snippet is from Wikipedia (Dated: Jan 2021):
Paracetamol, also known as acetaminophen, is a medication used to treat pain and fever. It is typically used for mild to moderate pain relief. Evidence is mixed for its use to relieve fever in children. It is often sold in combination with other medications, such as in many cold medications. Paracetamol is also used for severe pain, such as cancer pain and pain after surgery, in combination with opioid pain medication. It is typically used either by mouth or rectally, but is also available by injection into a vein. Effects last between two and four hours.

Paracetamol was first made in 1877. It is the most commonly used medication for pain and fever in both the United States and Europe. It is on the World Health Organization's List of Essential Medicines. Paracetamol is available as a generic medication, with brand names including Tylenol and Panadol among others. In 2017, it was the 25th-most commonly prescribed medication in the United States, with more than 24 million prescriptions.

Paracetamol is generally safe at recommended doses. The recommended maximum daily dose for an adult is three to four grams. Higher doses may lead to toxicity, including liver failure. Serious skin rashes may rarely occur. It appears to be safe during pregnancy and when breastfeeding. In those with liver disease, it may still be used, but in lower doses. It is classified as a mild analgesic. It does not have significant anti-inflammatory activity.
Paracetamol's mechanism of action is not entirely clear.

References:
% 1 "Despite its long history and widespread use, paracetamol has no known endogenous binding sites and uncertainty persists regarding its mechanism and action."

McKay GA, Walters MR (2013). "Non-Opioid Analgesics". Lecture Notes Clinical Pharmacology and Therapeutics (9th ed.). Hoboken: Wiley. ISBN 9781118344897. Archived from the original on 8 September 2017. Retrieved 7 September 2017. [ Link ]

% 2 "In the U.S., approximately 79% of the general population consume APAP (or Acetaminophen) regularly (Link)."

In addition to its antipyretic properties, APAP also produce analgesia. Several studies indicate that these two pharmacological outcomes occur through distinct mechanisms. Recently, a newly proposed mechanism of action for the analgesic properties of APAP has been described, which involves modulation of the endogenous cannabinoid system. This mechanism may provide an explanation for the “relaxation” or “calming” effect that has been reported in some patients that consume APAP. This effect is characterized by a peculiar sense of well-being, relaxation and tranquility. 

Note: Endocannabinoids are molecules that, like the plant cannabinoid THC, bind to and activate cannabinoid receptors. Endocannabinoids are produced naturally by cells in the human body (“endo” means “within,” as in within the body). The human body produces its own endogenous cannabinoids: natural equivalents of the compounds found in the cannabis plant, such as THC (tetrahydrocannabinol) and CBD (cannabidiol). 

Cannabinoid receptors, located throughout the body, are part of the endocannabinoid system, which is involved in a variety of physiological processes including appetite, pain-sensation, mood, and memory. Cannabinoid receptors are of a class of cell membrane receptors in the G protein-coupled receptor superfamily.

Info:
Ghanem CI, Pérez MJ, Manautou JE, Mottino AD (July 2016). "Acetaminophen from liver to brain: New insights into drug pharmacological action and toxicity". Pharmacological Research. 109: 119–31. doi:10.1016/j.phrs.2016.02.020. PMC 4912877. PMID 26921661. [ Link ]

%3 "Acetaminophen, an analgesic (painkiller) that does not inhibit prostaglandin synthesis, lacks a systematic anti-inflammatory effect. In contrast to aspirin and other NSAIDs, acetaminophen does not affect systemic PgE2 concentrations. However, acetaminophen has some structural similarity to steroids and may have an anti-estrogenic effect, lowering follicular levels of LH, FSH, and estradiol."

Viswanathan AN, Feskanich D, Schernhammer ES, Hankinson SE (2008). "Aspirin, NSAID, and Acetaminophen Use and the Risk of Endometrial Cancer". Cancer Research. 68 (7): 2507–2513. doi:10.1158/0008-5472.CAN-07-6257. PMC 2857531. PMID 18381460. [ Link ]

Another Reference: HealthDirect: By Government of Australia

How does paracetamol work?

Paracetamol has been in general use for more than 50 years, but the way it works to reduce pain and fever is not fully understood. Paracetamol begins to ease pain and lower a high temperature about 30 minutes after a dose is taken. Its effects usually last for about 4 to 6 hours.