That date would have to come from the state archives. If the legislature incorporated volunteer militia companies, that date can be found in the Mississippi House Journal. Each volume contains an index, so it shouldn't be too difficult to search.
Officers of antebellum militia companies like this one received commissions signed by the state governor. Copies of these and/or requests to issue commissions based on certified election results ought to be in the governor's correspondence. You can also check the state adjutant general's records for correspondence, muster rolls, commissions &c.
All of this ought to be easier than reading through Natchez newspapers for the relevant period. However, if the company existed at a particular time, it ought not be too difficult to spot public notices concerning company business meetings, drills and other anouncements.
Dates usually found for a volunteer unit in National Archives records include the date of organization. Bear in mind that this date will not be the date the company first formed. Volunteer militia companies normally reorganized and held new officer elections prior to offering their services to the governor. The captain usually wrote the governor to make an offer of service. The governor could accept or decline, depending on terms and conditions. For instance, the governor might decline if the offer was for a term less than twelve months or if the company needed arms and none were available in state armories.
Acceptance was important because without it (and their commisions, showing proper authority) the company could not be paid for service or draw on state quartermasters or commissaries. The governor then notified the company captain when and where his company would be required to report. Pay was dated from the date of acceptance or the date the company was called into service, usually the date of marching orders.
You will also see a date of acceptance in Confederate service. In the early days the governor assembled enough companies to form a regiment or battalion, and then notified the Confederate Secretary of War that he was offering the command for military service. The Secretary of War needed a muster roll for each company to certify the proper number of officers and men on roll. Usually these muster rolls were drawn up after companies reported to camp. Remember that the date and place of the muster roll isn't the same as the date and place of organization, nor is it the date and place of acceptance. Usually Confederate authorities would recognize a company from the date it was accepted in state service for purposes of pay and seniority.
I hope this makes a little sense. I'm sure with time and effort this could be made a little more clear. Over the past eighteen years I have made a study of Confederate organizational practices and the laws which governed them. Even people who spend years studying a particular unit seem to zip right past organizational events and issues.