Carrying Four Amos in a Public Domain
One need not cross from indoors to outdoors to perform hotza'ah. Carrying an object four amos within a reshus harabim is itself forbidden.
The measure of four amos
Four amos is measured according to halachic dimensions, not by an ordinary stride. The precise measurement follows the halachic amah and is not safely estimated by taking four casual steps.
Repeatedly putting an object down does not provide a routine way to move it through the street. Depending on how it is done, the person may complete the Torah prohibition or violate the rabbinic prohibition against carrying in shorter stages.
Ordinary objects
A key, tissue, child's item, siddur, or food container is an object for these halachos. Its small size or mitzvah use does not remove the prohibition.
The rule also applies to something carried for another person and to an item that has no financial value. The melacha concerns moving the object through the domain, not whether the person considers it important.
No doorway is required
Someone already standing in the street can perform hotza'ah by walking four amos with an object. The prohibition is therefore relevant to an item found on the sidewalk, something handed over outdoors, or an object removed from a stroller while still in the street.
This form of hotza'ah is one reason that remaining outdoors for the entire act does not make carrying permissible.