Logical argument mostly, though that gets less possible as the arguments in favor of Christianity become less about rigorous application of logic and more about historical fact and what you believe occurred 2000 years ago. Luckily going through the first steps necessarily opens your mind to the possibility that Jesus was indeed resurrected in violation of "natural" physical law and makes the last jump easier, though of all the tenets of Christianity the truth of the resurrection is probably the one that requires the biggest leap of "faith". Most other tenets are logically rock solid and defensible. Ed Feser has a good article here and he's a great starting point for a philosophically rigorous defense of Christianity. Generally I find there are steps in coming across from atheism to classical theism.
This is the first step which it seems like you've taken by accepting that ideas like love have a real, non-physical, existence. The existence of non-physical, qualitative aspects of reality leads one from the basis of atheistic thought that is naturalism to metaphysical assumptions that better support the existence of God as a transcendent, non-physical being from whom physical reality stems and continually upholds.
The next step is understanding the philosophical arguments for classical theism of which there are many. These arguments do not support any specific religion but serve to form the basis of acknowledging that there is indeed a God and it is a God consistent with what Christian doctrine considers God. There are the cosmological argument, the moral argument, the ontological argument and many others. Put together they make a persuasive, almost unassailable argument for the truth of theism. This is one of my favorite formulations.
The last step now that you've accepted theism as most likely the truth is to understand the arguments for why in all likelihood it is the trinitarian God of Christianity. The arguments for this are varied but one for example is that "love" necessitates that there be an other to be loved. Thus if God is love then the manifestation of that love would require that God exist as more than one person, both the lover and the beloved.