US would have no problem as they have most of resources needed for military, it would be the EU having more problems. US is as plentiful with resources as Russia. China actually has lower amount of resources than those two. We are of course talking about military materials like manganese, molybdenum, zinc, copper, titanium, aluminum, berillium, all the rare earth metals, chromium etc.
Lets take a look at the data.
1) Manganese: China has 6th largest reserves and is the second largest producer. US not a major source for manganese reserves nor production. Due to geographic distribution of reserves/production, both countries should have no problems sourcing manganese. Manganese is fairly common and found across an extensive variety of different ores.
2) Molybdenum: China has the largest reserves and is the largest producer. The US has the second largest reserves and is the third largest producer. Both countries are self sufficient.
4) Zinc: China has 2nd largest reserves and is the largest producer. While US is in top 10 in both reserves and production, US reserves are about 1/4th of China's and production less than 1/6th. Zinc is an generally common metal.
5) Copper: China has 6th largest reserves, 3rd largest production. US has 5th largest reserves, 4th largest production. Copper is a common metal with generally even geographic distribution.
6) Titanium: China has the largest reserves and is the largest producer. US has neither major reserves nor is a major producer, having to import titanium since the Cold War from the USSR under guise of making pizza ovens. Titanium itself is actually extremely abundant, the bottleneck being more technological and industrial in nature, titanium being one of the most difficult ores to process and refine. While Australia is a major source of Titanium ore, the US would need to rely on Japanese refining/processing until it can build up domestic capacity. Japan has no significant titanium reserves, so relying on Japanese production would require both Titanium ore to reach Japan and for finished Titanium to be able to depart from Japan.
7) Aluminum: China is 7th in Bauxite/Alumina reserves and produces over half of the world's aluminum. US has negligible discovered reserves, and despite being the 6th largest producer, produces not even 1/20th of the amount of China. Until production is scaled up, US will need to rely on Canadian and Norwegian aluminum production, and will need to limit aluminum consumption. Aluminum is extremely abundant, main limits to extractions and production are purely economical.
8) Chromium: Neither US nor China have a significant share of Chromium reserves nor are major Chromium producers. China used to maintain a fairly substantial amount of Chromium extraction and production, but due to environmental reasons switched to sourcing from foreign sources. Chromium itself is rather abundant, but economically viable deposits are not evenly distributed geographically. Chromium mining and production is associated with high levels of environmental degradation (even compared to the extraction/production of other metals). China can rely solely on friendly countries with which it shares a land border, as Russia and Kazakhstan are both major producers. Sources available to the US would be South Africa, Turkey, and India.
9) Rare earths: China has largest reserves and is the largest producer. US has 7th largest reserves, about 1/20th of China's, and is the 2nd largest producer (1/5th of China's). US might be able to source enough rare earths for military production, but it's economy as a whole will definitely lack sufficient rare earths, as China has the largest global reserves and controls over 60% of global rare earths production.
Another not listed, Tungsten is the metal that will be the biggest headache for US (and basically any nation other than China) to source. Tungsten is actually a rare metal, and is less common than all of the materials you have listed. Furthermore, the geographic distribution of viable tungsten reserves is extremely skewed. China controls both 90% of the world's reserves and production. Unlike many of the metals you have listed, Tungsten is absolutely critical in many military applications, where there are no existing substitutes. For example, until alternative composite/non-metal materials are developed, it is not possible to produce hypersonic weapons/aircraft without tungsten.
With the exception of titanium (which the US would experience difficulty in sourcing, at least initially), both countries are fairly sufficient (from purely military use perspective) in the resources you listed. For most the resources, China has an advantage in both proven reserves and production, and would enjoy an advantage in the cost and ease of sourcing. China would not need to rely on sea routes for any of these materials. The US will would need to rely on sea routes for at least a significant portion of several of these materials. Moving beyond military applications, the US would need to ramp up production in several of these materials, either domestically or in friendly countries with which the US has relatively secure shipping routes, in order to sustain civilian consumption. China has access to enough reserves and production capacity either domestically (all of the materials with exception of Chromium) or in friendly neighboring countries to sustain even civilian consumption for all of these materials indefinitely.
(The availability of reserves and current production only paint a high level overview. Actual extraction and production capability is heavily shaped by economic, technological, and environmental considerations. The difficulty, cost, and time required to scale up extraction and production also vary significant between types of ores. Even for a particular metal, the cost/difficulty of extraction should not be viewed as a set of discrete points, but rather across a continuum in terms of cost and economic viability which changes over time. A key and very critical exception to this rule is Tungsten, which forms in under extremely specific geological conditions.)