No.
The Apple Watch cellular uses the iPhone's phone number. For this service, the cellular companies that support the Apple Watch charge a monthly fee of about $10 U.S. added to the iPhone cellular bill. If you do not have an iPhone, or the iPhone does not have a cellular plan that supports the Apple Watch, then you cannot enable the cellular on the Apple Watch.
The alternative is to behave as the dependent child to another person, or the elderly relative of another person, and use the Apple Watch Family Plan
Apple Watch Family Plan
Set up Apple Watch for a family member - Apple Support
Set up Apple Watch For Your Kids - Apple Support
Some limitations: Cannot receive SMS/MMS messages, as that depends on a fully paired iPhone. Messaging is pretty much limited to Apple's Messages, unless the messaging service provides an Apple Watch app. Alarms, alerts, notifications on the iPhone are not sent to the Apple Watch. Apple Pay via a credit card is not available. Also not available: Medications, respiratory rate, irregular heart rhythm notifications, ECG, AFib History, Cycle Tracking, Sleep, Wrist Temperature, Blood Oxygen, Walking Steadiness, Audiobooks, Camera Remote, News, Shortcuts, and the double tap gesture.
