There is no per se age. As the Texas Penal Code states below, it's a crime to abandon a child under the age of 15 in any place under circumstances that expose the child to
an unreasonable risk of harm. That includes a home. It's a very subjective issue, each case depends on the details.
Texas Penal Code § 22.041. ABANDONING OR ENDANGERING CHILD. (a) In this
section, "abandon" means to leave a child in any place without
providing reasonable and necessary care for the child, under
circumstances under which no reasonable, similarly situated adult
would leave a child of that age and ability.
(b) A person commits an offense if, having custody, care, or
control of a child younger than 15 years, he intentionally abandons
the child in any place under circumstances that expose the child to
an unreasonable risk of harm.
(c) A person commits an offense if he intentionally,
knowingly, recklessly, or with criminal negligence, by act or
omission, engages in conduct that places a child younger than 15
years in imminent danger of death, bodily injury, or physical or
mental impairment.
(c-1) For purposes of Subsection (c), it is presumed that a
person engaged in conduct that places a child in imminent danger of
death, bodily injury, or physical or mental impairment if the
person manufactured the controlled substance methamphetamine in
the presence of the child.
(d) Except as provided by Subsection (e), an offense under
Subsection (b) is:
(1) a state jail felony if the actor abandoned the
child with intent to return for the child; or
(2) a felony of the third degree if the actor abandoned
the child without intent to return for the child.
(e) An offense under Subsection (b) is a felony of the
second degree if the actor abandons the child under circumstances
that a reasonable person would believe would place the child in
imminent danger of death, bodily injury, or physical or mental
impairment.
(f) An offense under Subsection (c) is a state jail felony.
(g) It is a defense to prosecution under Subsection (c) that
the act or omission enables the child to practice for or participate
in an organized athletic event and that appropriate safety
equipment and procedures are employed in the event.
(h) It is an exception to the application of this section
that the actor voluntarily delivered the child to a designated
emergency infant care provider under Section 262.302, Family Code.