The answer is - very little.
A highly intelligent and motivated individual can get 'up to speed' in a subject, and begin work in it, in a matter of weeks.
Of course it takes much longer than this to make a significant contribution to a field - often ten years or so of persistence - but this is why it is very important to get started young working on your problem. And starting young means skipping the hyper-extended specialist preliminary 'training' which is the norm nowadays.
This is obvious from the fact that early scientists had never had any formal specialist training because it did not exist.
Further evidence comes from the example of the many physicists and mathematicians who changed field and made major contributions to, for example, biology. They were able to do so because physicists and mathematicians are the most intelligent people (i.e. the group with the highest average general intelligence or IQ) - which means they can learn and remember new material extremely rapidly compared with most of us.
Of course, modern academia insists (usually) on prolonged specialist training. But this is mostly due to careerism and restrictive practices. Major work is continually being done in biology and medicine by people without this training, indeed many of the best ideas come from outside of academia, and often from clever and motivated amateurs (such as investigative journalists). Much of this is published outside the professional literature – in books, not papers.
Intelligence is mostly inborn (i.e. the ability to reason abstractly and systematically cannot be inculcated but is - mostly - either there, or not there); and the extra discipline and baseline knowledge which is provided by education is mostly acquired during development - before college age.
So, whatever formal specialist training a scientist needs before tackling his problem ought to be done at school, in the teenage years - and *not* done at college, in the twenties.