Simply, Oswald never expected to get out of the TSBD alive and had no game plan. Everything after the killing was spontaneous. He left Marina money and his wedding ring for a reason. He never expected to see her again. This is conscientious of guilt and common sense based on the evidence.
When finally apprehended, he lied all weekend to DPD and his own brother with ? Don?t believe the evidence? comment. It?s the best he could come up with.
Having just killed the President, Oswald, who didn't expect to get out of the TSBD alive, suddenly finds himself outside the building, free as a bird and being able to go anywhere.
But, rather than trying to escape he spontaneously decides not to do so and instead take a walk in Oak Cliff.....
Yeah right, as if that makes a lot of sense