I find it hard to believe that an absolute morality exists outside of our own subjective mind.
That is not a topic for Ethics, but for Epistemology. (your claim that we have “subjective minds”). The claim that Objectivist Ethics is objective is based on the premise that Reason, the faculty which integrates man’s senses is, if used properly, objective, and on the premise that the reality we do perceive is itself absolute.
The idea that our minds are subjective is based either on the assumption that we cannot perceive reality directly (because it doesn’t exist, or because there’s something wrong with us), or that we don’t have the capacity to understand reality, and its order, and everything we consider true is in fact just unreliable speculation (that our logic and concepts are all silly wordplay, meant to put our puny minds at ease). Which of these do you subscribe to, that made you say our minds are subjective, and what proof do you have of it?
[Edit: I just mentioned that your ‘subjective mind’ claim pertains to epistemology because it’s necessary for my explanation, not to imply that we’re in the wrong section of the forum or anything]
Suppose it has, then how do you access it? If you claim to know what is good and evil, you must know the answer to this.
If it is your assumption that Objectivism holds morality to be a concrete part of the natural world (like some list of commandments edged in our DNA, or a tablet in a cave, whatever), that is false. Morality is an abstract concept.
You “access” (in reality determine, not access, since Ethics is the creation of the human mind) it by applying logic to what your senses tell you. Through an objective process of rational thought (which is defined in Objectivist Epistemology), Ayn Rand determined what is the metaphysical necessity of a man’s survival qua man. The result is Ethics, objective, and just as absolute as the reality of our existence as men. You don’t have to take her word for it that she is correct, you can read her reasoning. In fact it is required that you do, instead of accepting the results blindly, to have any use for it.