This will depend greatly on the type of product and the nature of the country itself. For example, a rapidly developing country in the tropics will enjoy an absolute advantage in growing things like bananas or flowers over a rapidly developing country in the Central Asia. A country's natural advantages will do much to determine what absolute advantages it will enjoy.
As the country develops, it may come to have a comparative advantage in some products. At first, its comparative advantage is likely to be based largely on cost. It is likely that workers in such a country could be put to work doing low-skill jobs in a factory without giving up much in the way of opportunity costs. This is in contrast to a rich country where taking (for example) people like software engineers, nurses, and accountants and putting them on factory floors would be a waste of their abilities and would therefore have high opportunity costs. In a developing country, most workers will not have other very valuable skills and the opportunity cost of using them as low-skilled workers will be very low.
So, a rapidly developing country's absolute advantages are likely to be determined by its natural advantages. As it develops, it is likely to enjoy a comparative advantage in low-skilled jobs making things for export to richer countries.