Antihydrogen, the bound state of a positron and an antiproton, is a uniquely well-suited system for testing fundamental symmetries between matter and antimatter. Experiments performed by the ALPHA collaboration have enabled measurements of the antihydrogen 1S-2S transition, hyperfine structure, and the interaction between this antiatom and gravity. The precision of these studies is ultimately limited by the rate at which trapped antihydrogen can be produced and accumulated.At ALPHA, antihydrogen atoms are synthesised by slowly merging cold non-neutral positron and antiproton plasmas in a Penning-Malmberg trap. A small fraction of the produced antiatoms is trapped in a magnetic minimum trap where antihydrogen experimentation occurs. Under these conditions, antihydrogen is predominantly formed through three-body recombination, a process in which the positron temperature is a key parameter governing production and trapping rates. While positrons cool through cyclotron radiation emission, they reach a lower temperature limit of approximately 15 K in the ALPHA-2 apparatus. To overcome this limit, the positrons were sympathetically cooled using laser-cooled Be+ ion plasmas, reducing their temperature to the sub-10 K regime.This talk will present the development and implementation of Be+-assisted antihydrogen production in the ALPHA experiment. The development of this technique required overcoming a number of experimental challenges, including the preparation of reproducible ion plasmas, long-term optical alignment through active beam stabilisation, and understanding mixed-species plasma dynamics in the presence of a radially asymmetric magnetic field. These developments culminated in the first demonstration of Be+-assisted antihydrogen synthesis and trapping. Subsequent optimisation of the technique produced a near eightfold increase in the antihydrogen trapping rate, enabling the accumulation of more than 15,000 trapped antihydrogen atoms in less than seven hours. The resulting increase in available antihydrogen has significantly enhanced the statistical reach of ALPHA's precision measurement programme.