You have actually anticipated Descartes himself in this question. After he established his own existence, as a mind, a thinking being, with the Cogito (I think therefore I am) he proceeded to ask about the sources of the concepts ("ideas" in his terms) in his mind.
But among these ideas, some appear to me to be innate, some adventitious, and others to be formed [or invented] by myself ... But again I may possibly persuade myself that all these ideas are of the nature of those which I term adventitious, or else that they are all innate, or all fictitious: for I have not yet clearly discovered their true origin.
Descartes was not easily convinced that he himself could not be - unconsciously, as in dreams - the source of all his ideas.
And as to the other reason, which is that these ideas must proceed from objects outside me, since they do not depend on my will, I do not find it any the more convincing. For just as these impulses of which I have spoken are found in me, notwithstanding that they do not always concur with my will, so perhaps there is in me some faculty fitted to produce these ideas without the assistance of any external things, even though it is not yet known by me; just as, apparently, they have hitherto always been found in me during sleep without the aid of any external objects.
What did convince Descartes that some of his ideas must indeed have a source external to himself, was the following causation principle:
For just as this mode of objective existence pertains to ideas by their proper nature, so does the mode of formal existence pertain tot he causes of those ideas ... And although it may be the case that one idea gives birth to another idea, that cannot continue to be so indefinitely; for in the end we must reach an idea whose cause shall be so to speak an archetype, in which the whole reality [or perfection] which is so to speak objectively [or by representation] in these ideas is contained formally [and really].
It was this causation principle (*) that was, then, what you called the second indubitable axiom. By invoking it, Descartes was, for the first time, able to convince himself that something existed outside of him. At least one being had to exist beyond himself, and this was God. It took a further series of arguments to convince Descartes that some other things, beside God, also existed outside of him.
(*) See also What were DesCartes's conceptions of objectivity & subjectivity?
(**) The quotes are from Descartes's Third Meditation