There is no easy way into professional chaplaincy, nor should there be. It is a serious profession that touches the lives of people in their most vulnerable moments. Solid preparation is only to be expected. However, I don't think that the formality of ordination should be that difficult.
Standards for chaplains vary depending on the institution and field. For example, hospice chaplains tend to have the lowest requirements, although that's not always a given, while military chaplaincy is likely the most stringent. Hospitals are all over the place on basic requirements. Often, if someone really wants to make a career of chaplaincy outside of the military, it's better to have more education as well as to be properly endorsed.
It's great to be part of a professional organization, like the Association of Professional Chaplains. However, being certified with this group includes having been ordained by a recognized religious body, which poses a problem for people not affiliated with an organized religion. Humanists in the United States can pursue chaplaincy through The Humanist Society, but what about everyone else? Someone might suggest the Unitarian Universalist Association, but the requirements for becoming an ordained and fellowshipped UU minister are rather onerous, on top of the standard requirements for professional chaplains. Unless you are really keen on being a Unitarian Universalist chaplain, coming from that perspective and representing that faith, you'd be better advised to look elsewhere. Another possibility, about which I have blogged before is The Chaplaincy Institute.
Perhaps the most direct route would be through the Universal Life Church. Yes, this is the church that's known for 'online ordination,' but hear me out. There are actually multiple organizations with some variation of the ULC name, including one based out of the northwestern United States that dominates Google results. That would be Universal Life Church Ministries, also known as the Universal Life Church monastery. That organization cannot help you with becoming a professional chaplain. For that, you need to go to the original Universal Life Church based out of Modesto, California, which was founded in 1962 by Rev Kirby J. Hensely, and which is now led by his son, Rev Andre Hensely.
The original ULC has a very humble, practically broken website, located at ulchq.org, and yes this is the church which is recognized by the Association of Professional Chaplains for endorsements. So, to start down the path to professional chaplaincy without all the stress and confusion of extra hurdles set forth by a denomination, get ordained with this ULC, then follow up with the Association of Professional Chaplains for exactly what they need from your ordaining body. Andre at the ULC will be able to sign off on a letter for you. That is, assuming you have met the other requirements of the APC.
The APC expects you to have a graduate degree in theology, social work, or psychology, along with 4 units of Clinical Pastoral Education. Really, you need these before ordination will even matter. The best route is probably to go for a Master of Divinity through an accredited seminary, obtaining the units of CPE along the way. A good seminary program will steer you in the right direction as you work to become a chaplain.
Now, if you already have the degree and CPE requirements fulfilled, but just lack ordination and professional certification, you know your options. Hopefully it's clear that the more direct route from there is probably the Universal Life Church based in Modesto.