I believe some home health agencies do hire new grads. I do not know how long the training is but I believe they will train you. You will meet nurses who have experience in it so you can keep their contact in case you need help, they could be one call away.
As for non-hospital jobs, there are skilled nursing homes, assisted living facilities, short term/long term rehab centers, rehab hospitals available to apply to. Some rehab hospitals have high acuity so could give you good experience because they sometimes get patients even from ICUs.
Community hospitals, even though they are hospitals, they are usually in rural areas or towns far from major or capital cities. They do not get as many patients as bigger hospitals do and may be a longer drive from home but it is worth a shot. You can still get medsurg, OR, L&D, ICU and even ED floor experience there. It is also a good place to start, you may even like it and want to stay. All the best!