ETH2 is rolling out in multiple phases. The first phase (typically called phase 0) is the minimal beacon chain. Does this chain already include block rewards? If not, what's the incentive to stake ETH in order to be an early ETH2 validator?
Technically the answer is no, there's no reward in Eth2 for simply producing a block. However, there are rewards for producing blocks that contain useful content. It is expected that all blocks will contain useful content (i.e., it is not hard to produce/acquire useful content) so therefore validators that propose blocks in Eth2 are expected to be rewarded.
A proposer receives rewards for including the following objects in a block:
PendingAttestation: these are typically derived from
SignedAggregateAndProofmessages collected from the network, they contain attestations (votes) from validators on their view of the chain. The proposer reward is based upon the number of unique validator attestations included in the block. These objects are very common and each block is expected to contain attestations from hundreds or thousands of validators.
ProposerSlashing: these objects are created when a validator produces two conflicting blocks. These objects should (hopefully) be uncommon, they are the result of a serious user or software error.
AttesterSlashing: like above, except they are created when one or more validators produce conflicting attestations. They should also be rare and are the result of a serious error.
Reference: Ethereum 2.0 Phase 0 -- The Beacon Chain (aka., "the spec"). Search for "
PROPOSER_REWARD_QUOTIENT" to find places where proposer rewards are allocated.
Cavet: the Eth2 spec is still evolving, this answer references spec v0.11.1 from April 2020