These are only finite within Earth. Add even modest solar system travel capabilities and a lot more resources open up. Mining asteroids is just one idea there.
We should certainly explore and hope to discover rich deposits of varied resources that are worth expending the time and energy to find, extract, and use. However, to our knowledge, asteroids probably consist of clay and silicate rocks, some containing nickel-iron[1]
If we accept the hypotheses of an expanding universe then we find ourselves in a pickle as our potentially infinite resources race out of our light cone faster than we can chase them.