  We consider spacetime initiated by a finite-sized initial boundary as a
generalization of the Hartle-Hawking no-boundary state. We study entanglement
entropy of matter state prepared by such spacetime. We find that the
entanglement entropy for large subregion is given either by the initial state
entanglement or the entanglement island, preventing the entropy to grow
arbitrarily large. Consequently, the entanglement entropy is always bounded
from above by the boundary area of the island, leading to an entropy bound in
terms of the island. The island $I$ is located in the analytically continued
spacetime, either at the bra or the ket part of the spacetime in
Schwinger-Keldysh formalism. The entanglement entropy is given by an average of
$complex$ pseudo generalized entropy for each entanglement island. We find a
necessary condition of the initial state to be consistent with the strong
sub-additivity, which requires that any probe degrees of freedom are thermally
entangled with the rest of the system. We then find a large parameter region
where the spacetime with finite-sized initial boundary, which does not have the
factorization puzzle at leading order, dominates over the Hartle-Hawking
no-boundary state or the bra-ket wormhole. Due to the absence of a moment of
time reflection symmetry, the island in our setup is a generalization of the
entanglement wedge, called pseudo entanglement wedge. In pseudo entanglement
wedge reconstruction, we consider reconstructing the bulk matter transition
matrix on $A\cup I$, from a fine-grained state on $A$. The bulk transition
matrix is given by a thermofield double state with a projection by the initial
state. We also provide an AdS/BCFT model by considering EOW branes with
corners. We also find the exponential hardness of such reconstruction task
using a generalization of Python's lunch conjecture to pseudo generalized
entropy.
