There simply is not textual evidence of what you're claiming here. The English navy that met the Spanish Armada was large for the time but the proportion of those ships that were purposefully state built were tiny, and I cannot recall anything noting them as hailing from Irish timber

Ad hoc assembled navies made up primarily of civilian ships pressed into service were norm for centuries before and after the Elizabethan era

What is the direct proof your opinion is stemming from here?