China may not have had much of anything in the silver mine department, but they had several trading partners who did - specifically Japan and the Spanish Empire via the silver mines of Mexico. In fact the majority of China's imported silver was coming from Japan, which is surprising since the islands are typically known for their mineral-poorness; yet, in spite of its lack of iron, they had a relative glut of precious metals for export all the way until the Tokugawa Shogunate shut it down. Thus, throughout the 16th and 17th centuries, both of these sources provided Ming China with a huge influx of silver.
But that doesn't answer you question as to why there was the push to adopt it. Well, that hearkens back to a problem that had gripped the not only the Ming and Qing, but all the way back to the Tang of the 8th and 9th centuries, which itself was a virtual repeat of the economic situation of the late Han in the Second Century... put briefly, it was that the Chinese imperial government seemed to have pretty much no idea how money worked, and was hopelessly hamstrung in its efforts to try to fix the resultant economic problems by a far-too-strict devotion to the solutions of the past.
Chinese coinage from essentially the Qin on down had been tied to the tael/tongbao-string system of copper coinage since they given up on cowrie shells back in thr Zhou Dynasty. The problem with the cash-string system was that there just wasn't enough copper to go around to effectively fund the government with. As I said, this had been an absolute millstone about the neck of the CHinese economy since the Sui/Tang times, and had been approached by various administrations with a variety of attempted fixes. Everything from imposing the death penalty on counterfeiters (a perennial favorite), to decreeing that bolts of silk were to be used as effective currency, to -gasp!- beginning to issue paper money... all in the name of trying to stem the gaping economic ulcer that was the Imperium's hopeless loyalty to the copper-currency system... and all equally doomed to quickly prove a massive failure in the face of a populace who was more than willing to operate on a black market free from meddling governmental interference, and the government's own officialdom's steadfast allegiant to graft and greed rather than the national good.
The Ming, like the Tang before it, did try to institute its own paper money system... but, like the Tang before it, that would prove to be an effort in futility. In spite of strict laws enacted by the Ming government forbidding the actual physical exchange of its paper currency for actual bullion, as well as the hoarding of said metal (save for certain approved items such as jewelry or holy statuettes and the like), nevertheless the whole paper money thing fell apart. By the end of the 14th century, in fact, theMing paper currency - legally protected though it was - had nevertheless fallen to 1/35th of its face-value in the actual marketplace... putting it right on par with such historical currency gems as the Continental or the Assignat.
Silver, then, seemed to be the perfect outlet for the long-suffering copper-based Chinese economy, since it provided a new reserve unit by which to - at least theoretically - stem or at least slacken the demand for the strained copper reserves. This official governmental stance was likely helped along by the individual economic decisions facing those most affected by external trade: the coastal populace who actually interfaced with the waiguoren. Silver, let's face it, was a much better unit of trade for the coastal traders because it was exchangeable and considered valuable by their trading partners - whereas Ming paper money? Oh that's nice, a sheet of paper... let me know when you're ready to trade something of actual value. Both the feiqian notes and the tongbao copper-strings had been so thoroughly devalued by longstanding deflationary tendencies that they we simply of no use to those wishing to routinely do business outside of the empire itself. Silver filled that gap. From /u/parksungjun in this post:
while the value of a unit of silver in China was dependent on Chinese monetary and fiscal policy, the value of a unit of silver for, say, a trader on the coast, would be the same market value as whatever the same amount of silver would be in Manila or Nagasaki or Malacca or anywhere else. In effect, if you were a trader, you had huge flexibility with silver metal that you did not with the paper currency: in case something happened to one environment or the other, you could simply keep your assets for use in the other environment. To that extent, there were essentially two separate silver markets, much like a Venn Diagram, the intersection being the Chinese traders with the Western, Japanese, and South Asian traders.
Where this seemingly benevolent interaction ran into roadbumps, however, was when one half of the dual-economy began to sputter and die. Since the Chinese Empire was still absolutely dependent of the whims of nature and its ever-mercurial river systems to support its economic systems, it really was only a matter of time until something - floods, droughts, locusts, whathaveyou - upset the proverbial apple-cart on that front.
And when that happened, what did the coastal traders - who unique among the Chinese populace routinely dealt in and traded with silver bullion directly, rather than the papper and/or copper domestic currency - do? Why, they battened down the hatches, of course, and converted as much of their wealth into bullion as possible - a currency that would maintain its worth, regardless of the turmoil in the interior or what the government sought to "impose" on its own currency. That, combined with the Ming government's (again) incomprehension of what we understand to be basic economic principles, did with silver what it had done with copper and paper: in the face of an economic crisis, just mint or import more! As such, in spite of silver's initial status as being worth 1 oz. to 1000 copper coins, the glut of silver into the Ming economy resulted in its once-exalted status being further and further devalued, until by the 17th century, from von Glahn:
The value of silver in terms of gold declined steadily through-out the first half of the seventeenth century, finally sinking to the prevailing international level exactly at the moment the Ming dynasty fell. During the early Qing period the value of silver in China once again rose above the international price, suggesting that the relative demand for silver had reached a low ebb precisely when, according to the crisis hypothesis, it should have peaked. The movement of the gold-silver exchange ratio, like the price movements, suggests a surfeit rather than a scarcity of silver in the last years of the Ming.
This reaching of parity with the international market in terms of silver's valuation, created yet more issues for both the Ming and later the Qing. Suddenly rather than an overvalued reserve currency accessible only by the government itself (theoretically), China found itself in the 17th and 18th centuries increasingly "vulnerable to fluctuations in the price and quantity of silver on the world market. This meant that China, once so self-sufficient and little affected by the small economies of its neighbors, was now subject to economic problems caused by factors utterly beyond its control" (Gruen, 2004). Nevertheless, in spite of the system's inherent and intractable problems, it would survive the Ming - much as it had the Tang and the Yuan before it - and emerge largely unchanged in the Qing Dynasty. The Qing would maintain the tongbao system virtually until its dissolution, with China's first truly "national" bank system only being established in 1897 as the Imperial Bank of China (Zhongguo tongshang yinhang 中國通商銀行) in Guangdong.
Gruen, Sarah (2004). The Chinese Monetary System: From Ancient Times to the Early Modern Period.
Mote, F.W. (1999). Imperial China: 900-1800.
Von Glahn, Richard (1996). "Myth and Reality of China's Seventeenth-Century Monetary Crisis."
