A new technique for buffer gas loading is described. This technique greatly extends the range of atoms and molecules that may be magnetically trapped at low temperature. The advance is made possible by the rapid removal of the buffer gas on a time scale one hundred times greater than in previous buffer gas loading experiments. A new cryogenic valve is developed and employed. The following benchmarks were attained in our first experimental run; approximately $10^{12}$ atoms with effective magnetic moments $\mu_{eff} \geq 3\mu_B$ were trapped and thermally isolated with near unit efficiency, ~ $10^{10} \mu_{eff} = 2\mu_B$ atoms were trapped and thermally isolated, and ~ $10^9$ $\mu_{eff}= 1\mu_B$ atoms were trapped, but without thermal isolation. For comparison, all previous buffer gas loading experiments that achieved thermal isolation after trapping were done with atoms having a magnetic moment of at least $6\mu_B$ . In our second run of the experiment, better temperature management allowed us to increase the number of trapped and thermally isolated $\mu_{eff} = 2\mu_B$ atoms to ~$10^{11}$ and trapped $\mu_{eff} = 1\mu_B$ atoms to ~ $10^{10}$. The performance of the present apparatus is limited by the presence of a desorbing helium film that compromises the vacuum in the cell after the bulk of the buffer gas is removed. Future improvements to address this problem are suggested that will likely allow for efficient trapping and thermal isolation of atoms and molecules with magnetic moments as low as 1$\mu_B$. Analysis of the trapping and pumping dynamics is presented.