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During the Temple Times, for the purpose of consumption, can any Jew butcher a kosher animal or must the animal be butchered by a Cohen or a Levi?

I would appreciate a rabbinical source.

I just thought that a cohen or levi would be more qualified or trained to slaughter than an yisraelite (for the purpose of sacredness, purity ...)

Any Jew, not necessarily a kohen or levi, can slaughter an animal, with few exceptions (Chullin 1:1):

הַכֹּל שׁוֹחֲטִין וּשְׁחִיטָתָן כְּשֵׁרָה, חוּץ מֵחֵרֵשׁ, שׁוֹטֶה, וְקָטָן, שֶׁמָּא יְקַלְקְלוּ בִשְׁחִיטָתָן

Anyone [may] slaughter - and his slaughter is valid - except for a deaf-mute, a shoteh [a person who exhibits signs demonstrating a lack of ability to think clearly], or a minor, lest they spoil the slaughter.

This is said about non-consecrated animals slaughtered to be eaten, but it is even the case for sacrificial animals (Zevachim 3:1):

כָּל הַפְּסוּלִין שֶׁשָּׁחֲטוּ, שְׁחִיטָתָן כְּשֵׁרָה. שֶׁהַשְּׁחִיטָה כְשֵׁרָה בְּזָרִים, בְּנָשִׁים, וּבַעֲבָדִים, וּבִטְמֵאִים

If people who are ineligible [to serve in the Temple] slaughtered [an offering], their slaughtering is valid, since slaughtering is valid if performed by non-priests, by women, by slaves, and by impure individuals.