Are you allowed to do your entire PPL on a medium-sized jet aircraft from day one?
It will not work in EASA for a variety of reasons. Of the top of my head:

Like Lnafziger mentioned, you will need to do at least 10 hours solo. Most jet engines (but the smallest such as the D-Jet) have a minimum required crew of two. Also, you are not allowed to switch airplanes in the PPL course (ie. fly solo with one airplane and dual with another see FCL.235) so you are stuck.
Most jet aircraft (and as far as I know all commercial ones) are multi-engine. You will need 70 hours PIC before you can receive instruction on multi-engine, and you cannot fly PIC before you have your PPL.
Multi-engine jet aircraft require a type rating, which has a lot of license pre-requisites before you are even allowed to enter the cabin: MCC, IR, MEP(land)

There are a few prerequisites specified in  Part-FCL about getting your first class or type rating, and to accomplish most of them you will need to have at least a PPL (eg IR(A), ATPL theory tests, hours PIC ,etc)

FCL.235 Skill test
(b) An applicant for the skill test shall have received flight instruction on the same
class or type of aircraft, or a group of balloons to be used for the skill test.
FCL.720.A Experience requirements and prerequisites for the issue of
class or type ratings — aeroplanes
Unless otherwise determined in the
operational suitability data established in accordance with Part-21,
an applicant for a  class or type rating shall comply with the
following experience requirements and prerequisites for the issue of
the relevant  rating:
(a) Single-pilot multi-engine aeroplanes. An
applicant for a first class or type rating on a single-pilot
multi-engine  aeroplane shall have completed at least 70 hours as PIC
on aeroplanes.
(b) Single-pilot high performance non-complex aeroplanes. Before starting flight training, &gt; an applicant for a first class or
type rating for a single-pilot aeroplane classified as a high performance aeroplane shall:
(1) have at least 200 hours of total flying experience, of which 70 hours as PIC on aeroplanes; and
[...]
(c) Single-pilot high performance complex aeroplanes.
Applicants for the issue of a first type rating for a complex single-
pilot aeroplane classified as a high performance aeroplane shall, in
addition to meeting the requirements of (b), have  fulfilled the
requirements for a multi-engine IR(A), as established in Subpart G.
[...]
(d) Multi-pilot aeroplanes [...] or comply with the following
requirements:
(1) have at least 70 hours of flight experience as PIC
on aeroplanes;
(2) hold a multi-engine IR(A);
(3) have passed the
ATPL(A) theoretical knowledge examinations in accordance with this
Part; and  [...]