Historically many have understood Gen 2 to be an expansion on the detail of Gen 1 – specifically the details of Day 6. This view sees the creation of Adam & Eve as expanding the brief description in Gen1:26 of the call to make man in the image and likeness of God. On closer reading there are contrasts worth considering:
|Genesis 1||Genesis 2|
|Man created to have dominion over all the earth v25||Man created in Eden and works exclusively there until the Fall v8|
|Trees were created on day Three v11||There was no vegetation till after Adam v5, 8-9|
|Birds were created on day Five v20 Animals were created on day Six prior to humans v24||Both birds and animals were formed after Adam v19|
|Humans commanded to reproduce v28||Adam seemingly only knew Eve after the Fall in Gen4:1. Note this failure to procreate is not mentioned as a sin (given the sheep had time to produce a lamb, some 5 odd months had passed since Adam & Eve’s creation presumably).|
The tense of the formation of animals in Gen2:19 is sometimes disputed. The NET notes provide the following comments:
“To harmonize the order of events with the chronology of chapter one, some translate the prefixed verb form with vav consecutive as a past perfect (“had formed,” cf. NIV) here. (In chapter one the creation of the animals preceded the creation of man; here the animals are created after the man.) However, it is unlikely that the Hebrew construction can be translated in this way in the middle of this pericope, for the criteria for unmarked temporal overlay are not present here. See S. R. Driver, A Treatise on the Use of the Tenses in Hebrew , 84-88, and especially R. Buth, “Methodological Collision between Source Criticism and Discourse Analysis,” Biblical Hebrew and Discourse Linguistics , 138-54. For a contrary viewpoint see IBHS 552-53 §33.2.3 and C. J. Collins, “The Wayyiqtol as ‘Pluperfect’: When and Why,” TynBul 46 (1995): 117-40.”
This analysis of the Hebrew as pointing to the wording being sequential is strongly supported by Hebrew scholars like M Heiser 
To quote another scholar on the Hebrew
“The combination of the Hebrew prefixed conjugation (the ‘imperfect’ or yiqtōl) preceded by an attached strong waw (ו). (The strong [a.k.a. ‘consecutive’, ‘conversive’] waw is distinguished from the normal copulative waw by a lengthening of the vowel under the waw from a šᵊwa וְ to a pataḥ וַ or qāmeṣ וָ and a doubling [with the dāgēš ּ] of the following consonant [except gutturals].) This construction commonly conveys past tense / time. It is frequently referred to by grammarians as the “waw-consecutive” form, the ‘preterite’ form, or the wayyiqtōl / vayyiqtōl form. Tense-based approaches to the Hebrew verb use other labels as well, such as “inverted future”. See IBHS §33, GKC §49a-g, §111; BHRG §21.2; J.-M. §47, §118.”
There seems little doubt that when there is no pressure to have a motivated reading, the form of the Hebrew means the animals in Eden were formed after Adam.
The natural reading of Genesis 1 and Genesis 2 is two separate creative events, one global and one localised.
 Eg Heiser, M. S., & Setterholm, V. M. (2013; 2013). In Glossary of Morpho-Syntactic Database Terminology. Lexham Press. Also Concise HALOT,
 Logos 6 exegetical guide to Gen2v19
 Michael S. Heiser and Vincent M. Setterholm, Glossary of Morpho-Syntactic Database Terminology (Lexham Press, 2013; 2013).