Can I get a driver's license as a tourist in the EU?

Unlikely. Though you can still go to driving schools at least in some countries.

The EU directive on driving licences provides:

Article 7

1. Driving licences shall be issued only to those applicants:

[...]

(e) who have their normal residence in the territory of the Member State issuing the licence, or can produce evidence that they have been studying there for at least six months

Article 12

For the purpose of this Directive, ‘normal residence’ means the place where a person usually lives, that is for at least 185 days in each calendar year, because of personal and occupational ties, or, in the case of a person with no occupational ties, because of personal ties which show close links between that person and the place where he is living.

However, the normal residence of a person whose occupational ties are in a different place from his personal ties and who consequently lives in turn in different places situated in two or more Member States shall be regarded as being the place of his personal ties, provided that such person returns there regularly. This last condition need not be met where the person is living in a Member State in order to carry out a task of a definite duration. Attendance at a university or school shall not imply transfer of normal residence.

I'll answer your question exclusively for Switzerland, as we are part of Europe but not the European Union and not all EU laws apply.

In short: No. According to the "Verkehrszulassungsverordnung"(VZV, Traffic Admission Ordinance) Article 5k for a person to be eligible for a learner permit or the full permit that person's place of residence must be within Switzerland. Place of residence is defined as

Der Wohnsitz einer Person befindet sich an dem Orte, wo sie sich mit der Absicht dauernden Verbleibens aufhält; der Aufenthalt zum Zweck der Ausbildung oder die Unterbringung einer Person in einer Erziehungs- oder Pflegeeinrichtung, einem Spital oder einer Strafanstalt begründet für sich allein keinen Wohnsitz

Under Article 23 A in the "Schweizerisches Zivilgesetzbuch" (Swiss civil code)

Which basically states that the place of residence is the place where the person intends to remain. Although if the stay is for the purpose of education/ training or the accommodation of a person in an educational or care facility, a hospital or a prison does not itself constitute a place of residence.

So in a little longer: No, unless you intend to remain here for one of the many reasons not listed above

The process in Ireland is as follows:

1. Pass a Driver Theory Test
2. Apply for a learner permit
3. Sign up with an approved driving school for at least 12 hours of practical training
4. Pass a practical test held by the Road Safety Authority
5. Apply for your licence.

Steps 2 and 4 are problematic at the moment due to the COVID pandemic. These will reopen soon but with severe backlogs. Allow a minimum of six months to obtain a licence.