Syllable breaks are not a phonetic entity, which is why on Wiktionary, the transcription "ˈet.t͡ʃe" actually appears between phonemic slashes, not phonetic brackets: "/ˈet.t͡ʃe/, [ˈɛtː͡ʃe]".

The reason for supposing there is a syllable break is because Latin phonotactics doesn't allow a long consonant sound to occur at the start or end of a syllable: e.g. you can't have a syllable like cce or ecc in Latin. (The words "hic" and "hoc" seem to have been pronounced with a long [kː] sound before a vowel, but this was probably simplified to short [k] before a consonant.) In other words, the syllable break is theoretical, not something you should be trying to pronounce.

In terms of pronunciation, what you have is as follows:

• An approach phase, where the tongue is put in place behind the alveolar ridge to articulate a postalveolar stop
• A hold phase, where the tongue is pressed firmly enough against the top of the mouth to block airflow. Since [tː͡ʃ] is a long consonant, the hold phase is maintained for a longer period of time than it is for the short counterpart [tʃ]
• A release phase. After the extended hold period, the stop portion of the affricate is released, meaning the tongue lets some air past it. Since [tː͡ʃ] is an affricate sound, the release involves audible frication: even though air is moving past the tongue, the tongue is positioned in such a way that it partially obstructs the airflow and produces a [ʃ] sound.

That's it. There's nothing in the middle of the hold phase that separates the "t" and "t͡ʃ" in "/ˈet.t͡ʃe/": despite the presence of a syllable break in the phonemic notation, it is not a stop followed by a distinct affricate /t͡ʃ/, but merely an extended affricate.

Syllable breaks are not a phonetic entity, which is why on Wiktionary, the transcription "ˈet.t͡ʃe" actually appears between phonemic slashes, not phonetic brackets: "/ˈet.t͡ʃe/, [ˈɛtː͡ʃe]".

The reason for supposing there is a syllable break is because Latin phonotactics doesn't allow a long consonant sound to occur at the start or end of a syllable: e.g. you can't have a syllable like cce or ecc in Latin. (The words "hic" and "hoc" seem to have been pronounced in Classical Latin with a long [kː] sound when followed by a word starting with a vowel, but this was probably simplified to short [k] before a consonant.) In other words, the syllable break is theoretical, not something you should be trying to pronounce.

In terms of pronunciation, what you have is as follows:

• An approach phase, where the tongue is put in place behind the alveolar ridge to articulate a postalveolar stop
• A hold phase, where the tongue is pressed firmly enough against the top of the mouth to block airflow. Since [tː͡ʃ] is a long consonant, the hold phase is maintained for a longer period of time than it is for the short counterpart [tʃ]
• A release phase. After the extended hold period, the stop portion of the affricate is released, meaning the tongue lets some air past it. Since [tː͡ʃ] is an affricate sound, the release involves audible frication: even though air is moving past the tongue, the tongue is positioned in such a way that it partially obstructs the airflow and produces a [ʃ] sound.

That's it. There's nothing in the middle of the hold phase that separates the "t" and "t͡ʃ" in "/ˈet.t͡ʃe/": despite the presence of a syllable break in the phonemic notation, it is not a stop followed by a distinct affricate /t͡ʃ/, but merely an extended affricate.